Faster access than browser!
185 relations: Absolute convergence, Adelic algebraic group, AKS primality test, Algebraic number field, Algebraic variety, Almost surely, American Institute of Mathematics, American Mathematical Society, Analytic continuation, Anatoly Karatsuba, Andrew Wiles, Argument of a function, Argument principle, Arithmetic zeta function, Arnaud Denjoy, Artin L-function, Artin's conjecture on primitive roots, Automorphic form, Automorphic L-function, Barry Mazur, Basel problem, Big O notation, Birch and Swinnerton-Dyer conjecture, Brady Haran, Bulletin of the American Mathematical Society, Cambridge University Press, Canonical quantization, Carl Ludwig Siegel, Cauchy principal value, Chebyshev function, Circolo Matematico di Palermo, Class number problem, Clay Mathematics Institute, Complex analysis, Complex number, Comptes rendus de l'Académie des Sciences, Conjecture, Cramér's conjecture, Crelle's Journal, Cyclotomic field, David Hilbert, Dedekind zeta function, Dirichlet eta function, Dirichlet L-function, Disquisitiones Arithmeticae, Divisor function, Dover Publications, Edmund Landau, Eigenform, Eigenvalues and eigenvectors, ..., Elliptic curve, Entire function, Equidimensionality, Euclidean domain, Euler product, Euler's totient function, Euler–Maclaurin formula, Euler–Mascheroni constant, Explicit formulae (L-function), Exponential integral, Farey sequence, Finite field, Frobenius endomorphism, Function (mathematics), Function field of an algebraic variety, Functional equation, G. H. Hardy, Gamma function, Generalized Riemann hypothesis, Goldbach's conjecture, Goldbach's weak conjecture, Goss zeta function, Grand Riemann hypothesis, Group theory, Harald Cramér, Hecke character, Herman te Riele, Hilbert's eighth problem, Hilbert's problems, Hilbert–Pólya conjecture, Ideal class group, Idoneal number, Ihara zeta function, Imaginary unit, Infinite product, Ivan Fesenko, Iwasawa theory, Jérôme Franel, Jean-Louis Nicolas, Jean-Marc Deshouillers, John Derbyshire, John Edensor Littlewood, John Wiley & Sons, Jonathan Keating, Journal de Mathématiques Pures et Appliquées, Journal of Number Theory, L-function, Landau's function, Laplace operator, Lee–Yang theorem, Lehmer pair, Leonhard Euler, Li's criterion, Lindelöf hypothesis, Liouville function, List of zeta functions, Local zeta-function, Logarithmic integral function, Lp space, Maier's theorem, Main conjecture of Iwasawa theory, Mathematics of Computation, Mathematische Annalen, Mathematische Zeitschrift, Möbius function, Möbius inversion formula, McGraw-Hill Education, Mellin transform, Mertens conjecture, Mertens function, Michael Berry (physicist), Millennium Prize Problems, Miller–Rabin primality test, Montgomery's pair correlation conjecture, Natural logarithm, Natural number, Noncommutative geometry, Normal distribution, Notices of the American Mathematical Society, Number theory, Odlyzko–Schönhage algorithm, On the Number of Primes Less Than a Given Magnitude, P-adic L-function, Pólya conjecture, Primality test, Prime gap, Prime number, Prime number theorem, Prime Obsession, Prime-counting function, Proceedings of the National Academy of Sciences of the United States of America, Publications Mathématiques de l'IHÉS, Pure mathematics, Quadratic Gauss sum, Quantum harmonic oscillator, Quasicrystal, Ramanujan graph, Ramanujan's ternary quadratic form, Random matrix, Random walk, Real analytic Eisenstein series, Real number, Redheffer matrix, Richard P. Brent, Riemann Xi function, Riemann zeta function, Riemann–Siegel formula, Riemann–Siegel theta function, Riesz function, Selberg trace formula, Selberg zeta function, Self-adjoint operator, Series (mathematics), Siegel zero, Sine, Skewes's number, Spectrum of a ring, Springer Science+Business Media, Symmetric group, Tate's thesis, Toshikazu Sunada, Totally real number field, Transactions of the American Mathematical Society, Uncertainty principle, Vacuous truth, Vinogradov's mean-value theorem, Weil conjectures, Weil's criterion, Yasutaka Ihara, YouTube, Z function, Zero of a function, Zeros and poles, ZetaGrid, 1 + 1 + 1 + 1 + ⋯. Expand index (135 more) »
Absolute convergence
In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite.
New!!: Riemann hypothesis and Absolute convergence · See more »
Adelic algebraic group
In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A.
New!!: Riemann hypothesis and Adelic algebraic group · See more »
AKS primality test
The AKS primality test (also known as Agrawal–Kayal–Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena, computer scientists at the Indian Institute of Technology Kanpur, on August 6, 2002, in a paper titled "PRIMES is in P".
New!!: Riemann hypothesis and AKS primality test · See more »
Algebraic number field
In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
New!!: Riemann hypothesis and Algebraic number field · See more »
Algebraic variety
Algebraic varieties are the central objects of study in algebraic geometry.
New!!: Riemann hypothesis and Algebraic variety · See more »
Almost surely
In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one.
New!!: Riemann hypothesis and Almost surely · See more »
American Institute of Mathematics
The American Institute of Mathematics (AIM) was founded in 1994 by John Fry, co-founder of Fry's Electronics, and located in the Fry's Electronics San Jose, California location.
New!!: Riemann hypothesis and American Institute of Mathematics · See more »
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
New!!: Riemann hypothesis and American Mathematical Society · See more »
Analytic continuation
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function.
New!!: Riemann hypothesis and Analytic continuation · See more »
Anatoly Karatsuba
Anatoly Alexeevitch Karatsuba (Анато́лий Алексе́евич Карацу́ба; Grozny, Soviet Union, January 31, 1937 – Moscow, Russia, September 28, 2008) was a Russian mathematician working in the field of analytic number theory, ''p''-adic numbers and Dirichlet series.
New!!: Riemann hypothesis and Anatoly Karatsuba · See more »
Andrew Wiles
Sir Andrew John Wiles (born 11 April 1953) is a British mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory.
New!!: Riemann hypothesis and Andrew Wiles · See more »
Argument of a function
In mathematics, an argument of a function is a specific input in the function, also known as an independent variable.
New!!: Riemann hypothesis and Argument of a function · See more »
Argument principle
In complex analysis, the argument principle (or Cauchy's argument principle) relates the difference between the number of zeros and poles of a meromorphic function to a contour integral of the function's logarithmic derivative.
New!!: Riemann hypothesis and Argument principle · See more »
Arithmetic zeta function
In mathematics, the arithmetic zeta function is a zeta function associated with a scheme of finite type over integers.
New!!: Riemann hypothesis and Arithmetic zeta function · See more »
Arnaud Denjoy
Arnaud Denjoy (1884–1974) was a French mathematician.
New!!: Riemann hypothesis and Arnaud Denjoy · See more »
Artin L-function
In mathematics, an Artin L-function is a type of Dirichlet series associated to a linear representation ρ of a Galois group G. These functions were introduced in the 1923 by Emil Artin, in connection with his research into class field theory.
New!!: Riemann hypothesis and Artin L-function · See more »
Artin's conjecture on primitive roots
In number theory, Artin's conjecture on primitive roots states that a given integer a which is neither a perfect square nor −1 is a primitive root modulo infinitely many primes p. The conjecture also ascribes an asymptotic density to these primes.
New!!: Riemann hypothesis and Artin's conjecture on primitive roots · See more »
Automorphic form
In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of the topological group.
New!!: Riemann hypothesis and Automorphic form · See more »
Automorphic L-function
In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic form π of a reductive group G over a global field and a finite-dimensional complex representation r of the Langlands dual group LG of G, generalizing the Dirichlet L-series of a Dirichlet character and the Mellin transform of a modular form.
New!!: Riemann hypothesis and Automorphic L-function · See more »
Barry Mazur
Barry Charles Mazur (born December 19, 1937) is an American mathematician and a Gerhard Gade University Professor at Harvard University.
New!!: Riemann hypothesis and Barry Mazur · See more »
Basel problem
The Basel problem is a problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1734 and read on 5 December 1735 in ''The Saint Petersburg Academy of Sciences''.
New!!: Riemann hypothesis and Basel problem · See more »
Big O notation
Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.
New!!: Riemann hypothesis and Big O notation · See more »
Birch and Swinnerton-Dyer conjecture
In mathematics, the Birch and Swinnerton-Dyer conjecture describes the set of rational solutions to equations defining an elliptic curve.
New!!: Riemann hypothesis and Birch and Swinnerton-Dyer conjecture · See more »
Brady Haran
Brady John Haran (born 18 June 1976) is an Australian-born British independent filmmaker and video journalist who is known for his educational videos and documentary films produced for BBC News and his YouTube channels, the most notable being Periodic Videos and Numberphile.
New!!: Riemann hypothesis and Brady Haran · See more »
Bulletin of the American Mathematical Society
The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.
New!!: Riemann hypothesis and Bulletin of the American Mathematical Society · See more »
Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
New!!: Riemann hypothesis and Cambridge University Press · See more »
Canonical quantization
In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory, to the greatest extent possible.
New!!: Riemann hypothesis and Canonical quantization · See more »
Carl Ludwig Siegel
Carl Ludwig Siegel (December 31, 1896 – April 4, 1981) was a German mathematician specialising in number theory and celestial mechanics.
New!!: Riemann hypothesis and Carl Ludwig Siegel · See more »
Cauchy principal value
In mathematics, the Cauchy principal value, named after Augustin Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined.
New!!: Riemann hypothesis and Cauchy principal value · See more »
Chebyshev function
In mathematics, the Chebyshev function is either of two related functions.
New!!: Riemann hypothesis and Chebyshev function · See more »
Circolo Matematico di Palermo
The Circolo Matematico di Palermo (Mathematical Circle of Palermo) is an Italian mathematical society, founded in Palermo by Sicilian geometer Giovanni B. Guccia in 1884.
New!!: Riemann hypothesis and Circolo Matematico di Palermo · See more »
Class number problem
In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic fields \mathbb(\sqrt) (for negative integers d) having class number n. It is named after Carl Friedrich Gauss.
New!!: Riemann hypothesis and Class number problem · See more »
Clay Mathematics Institute
The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States.
New!!: Riemann hypothesis and Clay Mathematics Institute · See more »
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
New!!: Riemann hypothesis and Complex analysis · See more »
Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
New!!: Riemann hypothesis and Complex number · See more »
Comptes rendus de l'Académie des Sciences
Comptes rendus de l'Académie des Sciences (English: Proceedings of the Academy of sciences), or simply Comptes rendus, is a French scientific journal which has been published since 1666.
New!!: Riemann hypothesis and Comptes rendus de l'Académie des Sciences · See more »
Conjecture
In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof has been found.
New!!: Riemann hypothesis and Conjecture · See more »
Cramér's conjecture
In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they must be.
New!!: Riemann hypothesis and Cramér's conjecture · See more »
Crelle's Journal
Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).
New!!: Riemann hypothesis and Crelle's Journal · See more »
Cyclotomic field
In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to, the field of rational numbers.
New!!: Riemann hypothesis and Cyclotomic field · See more »
David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.
New!!: Riemann hypothesis and David Hilbert · See more »
Dedekind zeta function
In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζK(s), is a generalization of the Riemann zeta function (which is obtained in the case where K is the rational numbers Q).
New!!: Riemann hypothesis and Dedekind zeta function · See more »
Dirichlet eta function
In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part > 0: This Dirichlet series is the alternating sum corresponding to the Dirichlet series expansion of the Riemann zeta function, ζ(s) — and for this reason the Dirichlet eta function is also known as the alternating zeta function, also denoted ζ*(s).
New!!: Riemann hypothesis and Dirichlet eta function · See more »
Dirichlet L-function
In mathematics, a Dirichlet L-series is a function of the form Here χ is a Dirichlet character and s a complex variable with real part greater than 1.
New!!: Riemann hypothesis and Dirichlet L-function · See more »
Disquisitiones Arithmeticae
The Disquisitiones Arithmeticae (Latin for "Arithmetical Investigations") is a textbook of number theory written in Latin by Carl Friedrich Gauss in 1798 when Gauss was 21 and first published in 1801 when he was 24.
New!!: Riemann hypothesis and Disquisitiones Arithmeticae · See more »
Divisor function
In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer.
New!!: Riemann hypothesis and Divisor function · See more »
Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
New!!: Riemann hypothesis and Dover Publications · See more »
Edmund Landau
Edmund Georg Hermann Landau (14 February 1877 – 19 February 1938) was a German mathematician who worked in the fields of number theory and complex analysis.
New!!: Riemann hypothesis and Edmund Landau · See more »
Eigenform
An eigenform (meaning simultaneous Hecke eigenform with modular group SL(2,Z)) is a modular form which is an eigenvector for all Hecke operators Tm, m.
New!!: Riemann hypothesis and Eigenform · See more »
Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
New!!: Riemann hypothesis and Eigenvalues and eigenvectors · See more »
Elliptic curve
In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.
New!!: Riemann hypothesis and Elliptic curve · See more »
Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic at all finite points over the whole complex plane.
New!!: Riemann hypothesis and Entire function · See more »
Equidimensionality
In mathematics, especially in topology, equidimensionality is a property of a space that the local dimension is the same everywhere.
New!!: Riemann hypothesis and Equidimensionality · See more »
Euclidean domain
In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of the Euclidean division of the integers.
New!!: Riemann hypothesis and Euclidean domain · See more »
Euler product
In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers.
New!!: Riemann hypothesis and Euler product · See more »
Euler's totient function
In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to.
New!!: Riemann hypothesis and Euler's totient function · See more »
Euler–Maclaurin formula
In mathematics, the Euler–Maclaurin formula provides a powerful connection between integrals (see calculus) and sums.
New!!: Riemann hypothesis and Euler–Maclaurin formula · See more »
Euler–Mascheroni constant
The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma.
New!!: Riemann hypothesis and Euler–Mascheroni constant · See more »
Explicit formulae (L-function)
In mathematics, the explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by for the Riemann zeta function.
New!!: Riemann hypothesis and Explicit formulae (L-function) · See more »
Exponential integral
In mathematics, the exponential integral Ei is a special function on the complex plane.
New!!: Riemann hypothesis and Exponential integral · See more »
Farey sequence
In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions between 0 and 1 which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size.
New!!: Riemann hypothesis and Farey sequence · See more »
Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
New!!: Riemann hypothesis and Finite field · See more »
Frobenius endomorphism
In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic, an important class which includes finite fields.
New!!: Riemann hypothesis and Frobenius endomorphism · See more »
Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
New!!: Riemann hypothesis and Function (mathematics) · See more »
Function field of an algebraic variety
In algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex algebraic geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebraic geometry they are elements of some quotient ring's field of fractions.
New!!: Riemann hypothesis and Function field of an algebraic variety · See more »
Functional equation
In mathematics, a functional equation is any equation in which the unknown represents a function.
New!!: Riemann hypothesis and Functional equation · See more »
G. H. Hardy
Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis.
New!!: Riemann hypothesis and G. H. Hardy · See more »
Gamma function
In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.
New!!: Riemann hypothesis and Gamma function · See more »
Generalized Riemann hypothesis
The Riemann hypothesis is one of the most important conjectures in mathematics.
New!!: Riemann hypothesis and Generalized Riemann hypothesis · See more »
Goldbach's conjecture
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics.
New!!: Riemann hypothesis and Goldbach's conjecture · See more »
Goldbach's weak conjecture
In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that This conjecture is called "weak" because if Goldbach's strong conjecture (concerning sums of two primes) is proven, it would be true.
New!!: Riemann hypothesis and Goldbach's weak conjecture · See more »
Goss zeta function
In the field of mathematics, the Goss zeta function, named after David Goss, is an analogue of the Riemann zeta function for function fields.
New!!: Riemann hypothesis and Goss zeta function · See more »
Grand Riemann hypothesis
In mathematics, the grand Riemann hypothesis is a generalisation of the Riemann hypothesis and Generalized Riemann hypothesis.
New!!: Riemann hypothesis and Grand Riemann hypothesis · See more »
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
New!!: Riemann hypothesis and Group theory · See more »
Harald Cramér
Harald Cramér (25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory.
New!!: Riemann hypothesis and Harald Cramér · See more »
Hecke character
In number theory, a Hecke character is a generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of ''L''-functions larger than Dirichlet ''L''-functions, and a natural setting for the Dedekind zeta-functions and certain others which have functional equations analogous to that of the Riemann zeta-function.
New!!: Riemann hypothesis and Hecke character · See more »
Herman te Riele
Hermanus Johannes Joseph te Riele (born January 5, 1947, The Hague) is a mathematician at CWI in Amsterdam with a specialization in computational number theory.
New!!: Riemann hypothesis and Herman te Riele · See more »
Hilbert's eighth problem
Hilbert's eighth problem is one of David Hilbert's list of open mathematical problems posed in 1900.
New!!: Riemann hypothesis and Hilbert's eighth problem · See more »
Hilbert's problems
Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900.
New!!: Riemann hypothesis and Hilbert's problems · See more »
Hilbert–Pólya conjecture
In mathematics, the Hilbert–Pólya conjecture is a possible approach to the Riemann hypothesis, by means of spectral theory.
New!!: Riemann hypothesis and Hilbert–Pólya conjecture · See more »
Ideal class group
In number theory, the ideal class group (or class group) of an algebraic number field is the quotient group where is the group of fractional ideals of the ring of integers of, and is its subgroup of principal ideals.
New!!: Riemann hypothesis and Ideal class group · See more »
Idoneal number
In mathematics, Euler's idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers D such that any integer expressible in only one way as x2 ± Dy2 (where x2 is relatively prime to Dy2) is a prime, prime power, twice one of these, or a power of 2.
New!!: Riemann hypothesis and Idoneal number · See more »
Ihara zeta function
In mathematics, the Ihara zeta-function is a zeta function associated with a finite graph.
New!!: Riemann hypothesis and Ihara zeta function · See more »
Imaginary unit
The imaginary unit or unit imaginary number is a solution to the quadratic equation.
New!!: Riemann hypothesis and Imaginary unit · See more »
Infinite product
In mathematics, for a sequence of complex numbers a1, a2, a3,...
New!!: Riemann hypothesis and Infinite product · See more »
Ivan Fesenko
Ivan Fesenko is a mathematician working in number theory and its interaction with other areas of modern mathematics.
New!!: Riemann hypothesis and Ivan Fesenko · See more »
Iwasawa theory
In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields.
New!!: Riemann hypothesis and Iwasawa theory · See more »
Jérôme Franel
Jérôme Franel (1859–1939) was a Swiss mathematician who specialised in analytic number theory.
New!!: Riemann hypothesis and Jérôme Franel · See more »
Jean-Louis Nicolas
Jean-Louis Nicolas is a French number theorist.
New!!: Riemann hypothesis and Jean-Louis Nicolas · See more »
Jean-Marc Deshouillers
Jean-Marc Deshouillers (born on September 12, 1946 in Paris) is a French mathematician, specializing in analytic number theory.
New!!: Riemann hypothesis and Jean-Marc Deshouillers · See more »
John Derbyshire
John Derbyshire (born June 3, 1945) is a British-born American computer programmer, writer, journalist and political commentator.
New!!: Riemann hypothesis and John Derbyshire · See more »
John Edensor Littlewood
John Edensor Littlewood FRS LLD (9 June 1885 – 6 September 1977) was an English mathematician.
New!!: Riemann hypothesis and John Edensor Littlewood · See more »
John Wiley & Sons
John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.
New!!: Riemann hypothesis and John Wiley & Sons · See more »
Jonathan Keating
Jonathan Peter Keating FRS is a British mathematician.
New!!: Riemann hypothesis and Jonathan Keating · See more »
Journal de Mathématiques Pures et Appliquées
The Journal de Mathématiques Pures et Appliquées is a French monthly scientific journal of mathematics, founded in 1836 by Joseph Liouville (editor: 1836–1874).
New!!: Riemann hypothesis and Journal de Mathématiques Pures et Appliquées · See more »
Journal of Number Theory
The Journal of Number Theory is a mathematics journal that publishes a broad spectrum of original research in number theory.
New!!: Riemann hypothesis and Journal of Number Theory · See more »
L-function
In mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects.
New!!: Riemann hypothesis and L-function · See more »
Landau's function
In mathematics, Landau's function g(n), named after Edmund Landau, is defined for every natural number n to be the largest order of an element of the symmetric group Sn.
New!!: Riemann hypothesis and Landau's function · See more »
Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.
New!!: Riemann hypothesis and Laplace operator · See more »
Lee–Yang theorem
In statistical mechanics, the Lee–Yang theorem states that if partition functions of certain models in statistical field theory with ferromagnetic interactions are considered as functions of an external field, then all zeros are purely imaginary (or on the unit circle after a change of variable).
New!!: Riemann hypothesis and Lee–Yang theorem · See more »
Lehmer pair
In the study of the Riemann hypothesis, a Lehmer pair is a pair of zeros of the Riemann zeta function that are unusually close to each other.
New!!: Riemann hypothesis and Lehmer pair · See more »
Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
New!!: Riemann hypothesis and Leonhard Euler · See more »
Li's criterion
In number theory, Li's criterion is a particular statement about the positivity of a certain sequence that is equivalent to the Riemann hypothesis.
New!!: Riemann hypothesis and Li's criterion · See more »
Lindelöf hypothesis
In mathematics, the Lindelöf hypothesis is a conjecture by Finnish mathematician Ernst Leonard Lindelöf (see) about the rate of growth of the Riemann zeta function on the critical line.
New!!: Riemann hypothesis and Lindelöf hypothesis · See more »
Liouville function
The Liouville function, denoted by λ(n) and named after Joseph Liouville, is an important function in number theory.
New!!: Riemann hypothesis and Liouville function · See more »
List of zeta functions
In mathematics, a zeta function is (usually) a function analogous to the original example: the Riemann zeta function Zeta functions include.
New!!: Riemann hypothesis and List of zeta functions · See more »
Local zeta-function
In number theory, the local zeta function Z(V,s) (sometimes called the congruent zeta function) is defined as where N_m is the number of points of V defined over the degree m extension \mathbf_ of \mathbf_q, and V is a non-singular n-dimensional projective algebraic variety over the field \mathbf_q with q elements.
New!!: Riemann hypothesis and Local zeta-function · See more »
Logarithmic integral function
In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function.
New!!: Riemann hypothesis and Logarithmic integral function · See more »
Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
New!!: Riemann hypothesis and Lp space · See more »
Maier's theorem
In number theory, Maier's theorem is a theorem about the numbers of primes in short intervals for which Cramér's probabilistic model of primes gives the wrong answer.
New!!: Riemann hypothesis and Maier's theorem · See more »
Main conjecture of Iwasawa theory
In mathematics, the main conjecture of Iwasawa theory is a deep relationship between ''p''-adic ''L''-functions and ideal class groups of cyclotomic fields, proved by Kenkichi Iwasawa for primes satisfying the Kummer–Vandiver conjecture and proved for all primes by.
New!!: Riemann hypothesis and Main conjecture of Iwasawa theory · See more »
Mathematics of Computation
Mathematics of Computation is a bimonthly mathematics journal focused on computational mathematics.
New!!: Riemann hypothesis and Mathematics of Computation · See more »
Mathematische Annalen
Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.
New!!: Riemann hypothesis and Mathematische Annalen · See more »
Mathematische Zeitschrift
Mathematische Zeitschrift (German for Mathematical Journal) is a mathematical journal for pure and applied mathematics published by Springer Verlag.
New!!: Riemann hypothesis and Mathematische Zeitschrift · See more »
Möbius function
The classical Möbius function is an important multiplicative function in number theory and combinatorics.
New!!: Riemann hypothesis and Möbius function · See more »
Möbius inversion formula
In mathematics, the classic Möbius inversion formula was introduced into number theory during the 19th century by August Ferdinand Möbius.
New!!: Riemann hypothesis and Möbius inversion formula · See more »
McGraw-Hill Education
McGraw-Hill Education (MHE) is a learning science company and one of the "big three" educational publishers that provides customized educational content, software, and services for pre-K through postgraduate education.
New!!: Riemann hypothesis and McGraw-Hill Education · See more »
Mellin transform
In mathematics, the Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform.
New!!: Riemann hypothesis and Mellin transform · See more »
Mertens conjecture
In mathematics, the Mertens conjecture is the disproven statement that the Mertens function M(n) is bounded by \sqrt, which implies the Riemann hypothesis.
New!!: Riemann hypothesis and Mertens conjecture · See more »
Mertens function
In number theory, the Mertens function is defined for all positive integers n as where μ(k) is the Möbius function.
New!!: Riemann hypothesis and Mertens function · See more »
Michael Berry (physicist)
Sir Michael Victor Berry, (born 14 March 1941), is a mathematical physicist at the University of Bristol, England.
New!!: Riemann hypothesis and Michael Berry (physicist) · See more »
Millennium Prize Problems
The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.
New!!: Riemann hypothesis and Millennium Prize Problems · See more »
Miller–Rabin primality test
The Miller–Rabin primality test or Rabin–Miller primality test is a primality test: an algorithm which determines whether a given number is prime, similar to the Fermat primality test and the Solovay–Strassen primality test.
New!!: Riemann hypothesis and Miller–Rabin primality test · See more »
Montgomery's pair correlation conjecture
In mathematics, Montgomery's pair correlation conjecture is a conjecture made by that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit average spacing) is which, as Freeman Dyson pointed out to him, is the same as the pair correlation function of random Hermitian matrices.
New!!: Riemann hypothesis and Montgomery's pair correlation conjecture · See more »
Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.
New!!: Riemann hypothesis and Natural logarithm · See more »
Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
New!!: Riemann hypothesis and Natural number · See more »
Noncommutative geometry
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in some generalized sense).
New!!: Riemann hypothesis and Noncommutative geometry · See more »
Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.
New!!: Riemann hypothesis and Normal distribution · See more »
Notices of the American Mathematical Society
Notices of the American Mathematical Society is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue.
New!!: Riemann hypothesis and Notices of the American Mathematical Society · See more »
Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
New!!: Riemann hypothesis and Number theory · See more »
Odlyzko–Schönhage algorithm
In mathematics, the Odlyzko–Schönhage algorithm is a fast algorithm for evaluating the Riemann zeta function at many points, introduced by.
New!!: Riemann hypothesis and Odlyzko–Schönhage algorithm · See more »
On the Number of Primes Less Than a Given Magnitude
" die Anzahl der Primzahlen unter einer gegebenen " (usual English translation: "On the Number of Primes Less Than a Given Magnitude") is a seminal 10-page paper by Bernhard Riemann published in the November 1859 edition of the Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin.
New!!: Riemann hypothesis and On the Number of Primes Less Than a Given Magnitude · See more »
P-adic L-function
In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general ''L''-functions, but whose domain and target are p-adic (where p is a prime number).
New!!: Riemann hypothesis and P-adic L-function · See more »
Pólya conjecture
In number theory, the Pólya conjecture stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an odd number of prime factors.
New!!: Riemann hypothesis and Pólya conjecture · See more »
Primality test
A primality test is an algorithm for determining whether an input number is prime.
New!!: Riemann hypothesis and Primality test · See more »
Prime gap
A prime gap is the difference between two successive prime numbers.
New!!: Riemann hypothesis and Prime gap · See more »
Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
New!!: Riemann hypothesis and Prime number · See more »
Prime number theorem
In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.
New!!: Riemann hypothesis and Prime number theorem · See more »
Prime Obsession
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) is a historical book on mathematics by John Derbyshire, detailing the history of the Riemann hypothesis, named for Bernhard Riemann, and some of its applications.
New!!: Riemann hypothesis and Prime Obsession · See more »
Prime-counting function
In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by (x) (unrelated to the number pi).
New!!: Riemann hypothesis and Prime-counting function · See more »
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America (PNAS) is the official scientific journal of the National Academy of Sciences, published since 1915.
New!!: Riemann hypothesis and Proceedings of the National Academy of Sciences of the United States of America · See more »
Publications Mathématiques de l'IHÉS
Publications Mathématiques de l'IHÉS is a mathematical journal.
New!!: Riemann hypothesis and Publications Mathématiques de l'IHÉS · See more »
Pure mathematics
Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.
New!!: Riemann hypothesis and Pure mathematics · See more »
Quadratic Gauss sum
In number theory, quadratic Gauss sums are certain finite sums of roots of unity.
New!!: Riemann hypothesis and Quadratic Gauss sum · See more »
Quantum harmonic oscillator
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator.
New!!: Riemann hypothesis and Quantum harmonic oscillator · See more »
Quasicrystal
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic.
New!!: Riemann hypothesis and Quasicrystal · See more »
Ramanujan graph
In spectral graph theory, a Ramanujan graph, named after Srinivasa Ramanujan, is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory).
New!!: Riemann hypothesis and Ramanujan graph · See more »
Ramanujan's ternary quadratic form
In mathematics, in number theory, Ramanujan's ternary quadratic form is the algebraic expression with integral values for x, y and z.
New!!: Riemann hypothesis and Ramanujan's ternary quadratic form · See more »
Random matrix
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables.
New!!: Riemann hypothesis and Random matrix · See more »
Random walk
A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers.
New!!: Riemann hypothesis and Random walk · See more »
Real analytic Eisenstein series
In mathematics, the simplest real analytic Eisenstein series is a special function of two variables.
New!!: Riemann hypothesis and Real analytic Eisenstein series · See more »
Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
New!!: Riemann hypothesis and Real number · See more »
Redheffer matrix
In mathematics, a Redheffer matrix, studied by, is a (0,1) matrix whose entries aij are 1 if i divides j or if j.
New!!: Riemann hypothesis and Redheffer matrix · See more »
Richard P. Brent
Richard Peirce Brent (born 20 April 1946, Melbourne) is an Australian mathematician and computer scientist.
New!!: Riemann hypothesis and Richard P. Brent · See more »
Riemann Xi function
In mathematics, the Riemann Xi function is a variant of the Riemann zeta function, and is defined so as to have a particularly simple functional equation.
New!!: Riemann hypothesis and Riemann Xi function · See more »
Riemann zeta function
The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.
New!!: Riemann hypothesis and Riemann zeta function · See more »
Riemann–Siegel formula
In mathematics, the Riemann–Siegel formula is an asymptotic formula for the error of the approximate functional equation of the Riemann zeta function, an approximation of the zeta function by a sum of two finite Dirichlet series.
New!!: Riemann hypothesis and Riemann–Siegel formula · See more »
Riemann–Siegel theta function
In mathematics, the Riemann–Siegel theta function is defined in terms of the Gamma function as \Gamma\left(\frac\right) \right) - \frac t for real values of t. Here the argument is chosen in such a way that a continuous function is obtained and \theta(0).
New!!: Riemann hypothesis and Riemann–Siegel theta function · See more »
Riesz function
In mathematics, the Riesz function is an entire function defined by Marcel Riesz in connection with the Riemann hypothesis, by means of the power series If we set F(x).
New!!: Riemann hypothesis and Riesz function · See more »
Selberg trace formula
In mathematics, the Selberg trace formula, introduced by, is an expression for the character of the unitary representation of on the space of square-integrable functions, where is a Lie group and a cofinite discrete group.
New!!: Riemann hypothesis and Selberg trace formula · See more »
Selberg zeta function
The Selberg zeta-function was introduced by.
New!!: Riemann hypothesis and Selberg zeta function · See more »
Self-adjoint operator
In mathematics, a self-adjoint operator on a finite-dimensional complex vector space V with inner product \langle\cdot,\cdot\rangle is a linear map A (from V to itself) that is its own adjoint: \langle Av,w\rangle.
New!!: Riemann hypothesis and Self-adjoint operator · See more »
Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
New!!: Riemann hypothesis and Series (mathematics) · See more »
Siegel zero
In mathematics, more specifically in the field of analytic number theory, a Siegel zero, named after Carl Ludwig Siegel, is a type of potential counterexample to the generalized Riemann hypothesis, on the zeroes of Dirichlet L-function.
New!!: Riemann hypothesis and Siegel zero · See more »
Sine
In mathematics, the sine is a trigonometric function of an angle.
New!!: Riemann hypothesis and Sine · See more »
Skewes's number
In number theory, Skewes's number is any of several extremely large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number x for which where π is the prime-counting function and li is the logarithmic integral function.
New!!: Riemann hypothesis and Skewes's number · See more »
Spectrum of a ring
In abstract algebra and algebraic geometry, the spectrum of a commutative ring R, denoted by \operatorname(R), is the set of all prime ideals of R. It is commonly augmented with the Zariski topology and with a structure sheaf, turning it into a locally ringed space.
New!!: Riemann hypothesis and Spectrum of a ring · See more »
Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
New!!: Riemann hypothesis and Springer Science+Business Media · See more »
Symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.
New!!: Riemann hypothesis and Symmetric group · See more »
Tate's thesis
In number theory, Tate's thesis is the 1950 thesis of under supervision of Emil Artin.
New!!: Riemann hypothesis and Tate's thesis · See more »
Toshikazu Sunada
is a Japanese mathematician and author of many books and essays on mathematics and mathematical sciences.
New!!: Riemann hypothesis and Toshikazu Sunada · See more »
Totally real number field
In number theory, a number field K is called totally real if for each embedding of K into the complex numbers the image lies inside the real numbers.
New!!: Riemann hypothesis and Totally real number field · See more »
Transactions of the American Mathematical Society
The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.
New!!: Riemann hypothesis and Transactions of the American Mathematical Society · See more »
Uncertainty principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.
New!!: Riemann hypothesis and Uncertainty principle · See more »
Vacuous truth
In mathematics and logic, a vacuous truth is a statement that asserts that all members of the empty set have a certain property.
New!!: Riemann hypothesis and Vacuous truth · See more »
Vinogradov's mean-value theorem
In mathematics, Vinogradov's mean value theorem is an estimate for the number of equal sums of powers.
New!!: Riemann hypothesis and Vinogradov's mean-value theorem · See more »
Weil conjectures
In mathematics, the Weil conjectures were some highly influential proposals by on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields.
New!!: Riemann hypothesis and Weil conjectures · See more »
Weil's criterion
In mathematics, Weil's criterion is a criterion of André Weil for the Generalized Riemann hypothesis to be true.
New!!: Riemann hypothesis and Weil's criterion · See more »
Yasutaka Ihara
Yasutaka Ihara (伊原 康隆, Ihara Yasutaka; born 1938, Tokyo Prefecture) is a Japanese mathematician, professor emeritus at the Research Institute for Mathematical Sciences, working on number theory who introduced Ihara's lemma and the Ihara zeta function.
New!!: Riemann hypothesis and Yasutaka Ihara · See more »
YouTube
YouTube is an American video-sharing website headquartered in San Bruno, California.
New!!: Riemann hypothesis and YouTube · See more »
Z function
In mathematics, the Z-function is a function used for studying the Riemann zeta-function along the critical line where the argument is one-half.
New!!: Riemann hypothesis and Z function · See more »
Zero of a function
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).
New!!: Riemann hypothesis and Zero of a function · See more »
Zeros and poles
In mathematics, a zero of a function is a value such that.
New!!: Riemann hypothesis and Zeros and poles · See more »
ZetaGrid
ZetaGrid was at one time the largest distributed computing project designed to explore roots of the Riemann zeta function, checking over one billion roots a day.
New!!: Riemann hypothesis and ZetaGrid · See more »
1 + 1 + 1 + 1 + ⋯
In mathematics,, also written \sum_^ n^0, \sum_^ 1^n, or simply \sum_^ 1, is a divergent series, meaning that its sequence of partial sums does not converge to a limit in the real numbers.
New!!: Riemann hypothesis and 1 + 1 + 1 + 1 + ⋯ · See more »
Redirects here:
Critical line, Critical line theorem, Hardy-Littlewood-Selberg-Levinson-Conrey theorem, Hardy–Littlewood–Selberg–Levinson–Conrey theorem, Hilberts eighth problem, Lehmer's phenomenon, Reimann Hypothesis, Reimann hypothesis, Reimman hypothesis, Rieman hypothesis, Riemann Hypothesis, Riemann Zeta Hypothesis, Riemann Zeta hypothesis, Riemann conjecture, Riemann hypotheses, Riemann zeta hypothesis, Riemann zeta-hypothesis, Riemann's Hypothesis, Riemann's hypothesis, Riemman hypothesis, Selberg's theorem, Smale's first problem, The Riemann Hypothesis.
References
[1] https://en.wikipedia.org/wiki/Riemann_hypothesis
