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137 relations: Abel–Plana formula, Abramowitz and Stegun, Absolute convergence, American Mathematical Society, Analytic continuation, Analytic function, Analytic number theory, Anatoly Karatsuba, Apéry's constant, Argument (complex analysis), Arithmetic zeta function, Atle Selberg, Basel problem, Bernhard Riemann, Bernoulli number, Bose–Einstein condensate, Brady Haran, Canadian Mathematical Society, Casimir effect, Cauchy principal value, Chebyshev polynomials, Clay Mathematics Institute, Complex analysis, Complex number, Complex plane, Comptes rendus de l'Académie des Sciences, Conjecture, Convergent series, Coprime integers, Dedekind zeta function, Dirichlet eta function, Dirichlet L-function, Dirichlet series, Divergent series, Domain coloring, Dynamical system, Engel expansion, Euclid's theorem, Euler product, Euler summation, Euler–Mascheroni constant, Extended real number line, Falling and rising factorials, Function (mathematics), Functional equation, Fundamental theorem of arithmetic, G. H. Hardy, Gamma function, Gauss–Kuzmin–Wirsing operator, Generalized Riemann hypothesis, ..., Geometric series, Graduate Texts in Mathematics, Gregory coefficients, Hankel contour, Harmonic number, Harmonic series (mathematics), Helmut Hasse, Holomorphic function, Hurwitz zeta function, Infinite product, Jacques Hadamard, John Edensor Littlewood, Jordan's totient function, Joseph Ser, Journal of Number Theory, Kanakanahalli Ramachandra, Konrad Knopp, L-function, Lambert W function, Laurent series, Lehmer pair, Leonhard Euler, Lerch zeta function, Limit of a sequence, List of zeta functions, Mathematische Zeitschrift, Möbius function, Möbius inversion formula, Mellin transform, Meromorphic function, Modular form, Multiple zeta function, Multiplicative function, Natural density, On the Number of Primes Less Than a Given Magnitude, Oxford, Pafnuty Chebyshev, Particular values of the Riemann zeta function, Peter Borwein, Physics, Planck's law, Polygamma function, Polylogarithm, Power law, Prime number, Prime number theorem, Prime zeta function, Prime-counting function, Primorial, Probability theory, Proceedings of the American Mathematical Society, Proof of the Euler product formula for the Riemann zeta function, Pure mathematics, Quantum field theory, Rational number, Rational zeta series, Regularization (physics), Renormalization, Residue (complex analysis), Riemann hypothesis, Riemann Xi function, Riemann–Siegel formula, Riemann–Siegel theta function, Roger Apéry, Series (mathematics), Special values of L-functions, Spin wave, Statistics, Stefan–Boltzmann law, Stieltjes constants, Stirling numbers of the first kind, String theory, Theta function, Triviality (mathematics), Umbral calculus, Upper half-plane, Vinogradov's mean-value theorem, Weierstrass factorization theorem, Z function, Zero of a function, Zeros and poles, Zeta function regularization, Zeta function universality, Zipf's law, Zipf–Mandelbrot law, 1 + 1 + 1 + 1 + ⋯, 1 + 2 + 3 + 4 + ⋯. Expand index (87 more) »
Abel–Plana formula
In mathematics, the Abel–Plana formula is a summation formula discovered independently by and.
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Abramowitz and Stegun
Abramowitz and Stegun (AS) is the informal name of a mathematical reference work edited by Milton Abramowitz and Irene Stegun of the United States National Bureau of Standards (NBS), now the National Institute of Standards and Technology (NIST).
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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.
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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.
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Analytic continuation
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function.
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Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
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Analytic number theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.
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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.
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Apéry's constant
In mathematics, at the intersection of number theory and special functions, Apéry's constant is defined as the number where is the Riemann zeta function.
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Argument (complex analysis)
In mathematics, the argument is a multi-valued function operating on the nonzero complex numbers.
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Arithmetic zeta function
In mathematics, the arithmetic zeta function is a zeta function associated with a scheme of finite type over integers.
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Atle Selberg
Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory.
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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''.
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Bernhard Riemann
Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.
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Bernoulli number
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.
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Bose–Einstein condensate
A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero.
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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.
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Canadian Mathematical Society
The Canadian Mathematical Society (CMS) (Société mathématique du Canada) is an association of professional mathematicians dedicated to the interests of mathematical research, outreach, and scholarship and education in Canada.
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Casimir effect
In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field.
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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.
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Chebyshev polynomials
In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively.
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Clay Mathematics Institute
The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States.
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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.
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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.
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Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
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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.
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Conjecture
In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof has been found.
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Convergent series
In mathematics, a series is the sum of the terms of an infinite sequence of numbers.
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Coprime integers
In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.
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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).
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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).
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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.
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Dirichlet series
In mathematics, a Dirichlet series is any series of the form where s is complex, and a_n is a complex sequence.
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Divergent series
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.
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Domain coloring
In mathematics, domain coloring or a color wheel graph is a technique for visualizing complex functions, which assigns a color to each point of the complex plane.
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Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.
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Engel expansion
The Engel expansion of a positive real number x is the unique non-decreasing sequence of positive integers \ such that For instance, Euler's constant ''e'' has the Engel expansion corresponding to the infinite series Rational numbers have a finite Engel expansion, while irrational numbers have an infinite Engel expansion.
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Euclid's theorem
Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers.
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Euler product
In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers.
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Euler summation
In the mathematics of convergent and divergent series, Euler summation is a summability method.
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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.
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Extended real number line
In mathematics, the affinely extended real number system is obtained from the real number system by adding two elements: and (read as positive infinity and negative infinity respectively).
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Falling and rising factorials
In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as The rising factorial (sometimes called the Pochhammer function, Pochhammer polynomial, ascending factorial, (A reprint of the 1950 edition by Chelsea Publishing Co.) rising sequential product, or upper factorial) is defined as The value of each is taken to be 1 (an empty product) when n.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Functional equation
In mathematics, a functional equation is any equation in which the unknown represents a function.
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Fundamental theorem of arithmetic
In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.
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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.
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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.
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Gauss–Kuzmin–Wirsing operator
In mathematics, the Gauss–Kuzmin–Wirsing operator is the transfer operator of the Gauss map.
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Generalized Riemann hypothesis
The Riemann hypothesis is one of the most important conjectures in mathematics.
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Geometric series
In mathematics, a geometric series is a series with a constant ratio between successive terms.
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Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.
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Gregory coefficients
Gregory coefficients, also known as reciprocal logarithmic numbers, Bernoulli numbers of the second kind, or Cauchy numbers of the first kind,Ch.
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Hankel contour
In mathematics, a Hankel contour is a path in the complex plane which extends from, around the origin counter clockwise and back to, where δ is an arbitrarily small positive number.
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Harmonic number
In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: Harmonic numbers are related to the harmonic mean in that the -th harmonic number is also times the reciprocal of the harmonic mean of the first positive integers.
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Harmonic series (mathematics)
In mathematics, the harmonic series is the divergent infinite series: Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are,,, etc., of the string's fundamental wavelength.
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Helmut Hasse
Helmut Hasse (25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local class field theory and diophantine geometry (Hasse principle), and to local zeta functions.
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Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
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Hurwitz zeta function
In mathematics, the Hurwitz zeta function, named after Adolf Hurwitz, is one of the many zeta functions.
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Infinite product
In mathematics, for a sequence of complex numbers a1, a2, a3,...
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Jacques Hadamard
Jacques Salomon Hadamard ForMemRS (8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.
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John Edensor Littlewood
John Edensor Littlewood FRS LLD (9 June 1885 – 6 September 1977) was an English mathematician.
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Jordan's totient function
Let k be a positive integer.
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Joseph Ser
Joseph Ser (1875–1954) was a French mathematician, of whom little was known till now.
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Journal of Number Theory
The Journal of Number Theory is a mathematics journal that publishes a broad spectrum of original research in number theory.
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Kanakanahalli Ramachandra
Kanakanahalli Ramachandra (August 18, 1933 – January 17, 2011) was an Indian mathematician working in both analytic and algebraic theory of numbers.
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Konrad Knopp
Konrad Hermann Theodor Knopp (22 July 1882 – 20 April 1957) was a German mathematician who worked on generalized limits and complex functions.
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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.
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Lambert W function
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a set of functions, namely the branches of the inverse relation of the function f(z).
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Laurent series
In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree.
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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.
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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.
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Lerch zeta function
In mathematics, the Lerch zeta function, sometimes called the Hurwitz–Lerch zeta-function, is a special function that generalizes the Hurwitz zeta function and the polylogarithm.
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Limit of a sequence
As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.
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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.
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Mathematische Zeitschrift
Mathematische Zeitschrift (German for Mathematical Journal) is a mathematical journal for pure and applied mathematics published by Springer Verlag.
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Möbius function
The classical Möbius function is an important multiplicative function in number theory and combinatorics.
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Möbius inversion formula
In mathematics, the classic Möbius inversion formula was introduced into number theory during the 19th century by August Ferdinand Möbius.
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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.
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Meromorphic function
In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a discrete set of isolated points, which are poles of the function.
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Modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.
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Multiple zeta function
In mathematics, the multiple zeta functions are generalisations of the Riemann zeta function, defined by \zeta(s_1, \ldots, s_k).
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Multiplicative function
In number theory, a multiplicative function is an arithmetic function f(n) of a positive integer n with the property that f(1).
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Natural density
In number theory, natural density (or asymptotic density or arithmetic density) is one of the possibilities to measure how large a subset of the set of natural numbers is.
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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.
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Oxford
Oxford is a city in the South East region of England and the county town of Oxfordshire.
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Pafnuty Chebyshev
Pafnuty Lvovich Chebyshev (p) (–) was a Russian mathematician.
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Particular values of the Riemann zeta function
This article gives some specific values of the Riemann zeta function, including values at integer arguments, and some series involving them.
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Peter Borwein
Peter Benjamin Borwein (born St. Andrews, Scotland, May 10, 1953) is a Canadian mathematician and a professor at Simon Fraser University.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Planck's law
Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T. The law is named after Max Planck, who proposed it in 1900.
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Polygamma function
In mathematics, the polygamma function of order is a meromorphic function on '''ℂ''' and defined as the th derivative of the logarithm of the gamma function: Thus holds where is the digamma function and is the gamma function.
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Polylogarithm
In mathematics, the polylogarithm (also known as '''Jonquière's function''', for Alfred Jonquière) is a special function Lis(z) of order s and argument z. Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or rational functions.
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Power law
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another.
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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.
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Prime number theorem
In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.
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Prime zeta function
In mathematics, the prime zeta function is an analogue of the Riemann zeta function, studied by.
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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).
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Primorial
In mathematics, and more particularly in number theory, primorial is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, only prime numbers are multiplied.
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Probability theory
Probability theory is the branch of mathematics concerned with probability.
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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.
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Proof of the Euler product formula for the Riemann zeta function
Leonhard Euler proved the Euler product formula for the Riemann zeta function in his thesis Variae observationes circa series infinitas (Various Observations about Infinite Series), published by St Petersburg Academy in 1737.
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Pure mathematics
Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.
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Quantum field theory
In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Rational zeta series
In mathematics, a rational zeta series is the representation of an arbitrary real number in terms of a series consisting of rational numbers and the Riemann zeta function or the Hurwitz zeta function.
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Regularization (physics)
In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called regulator.
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Renormalization
Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of quantities to compensate for effects of their self-interactions.
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Residue (complex analysis)
In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities.
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Riemann hypothesis
In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.
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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.
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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.
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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).
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Roger Apéry
Roger Apéry (14 November 1916, Rouen – 18 December 1994, Caen) was a Greek-French mathematician most remembered for Apéry's theorem, which states that ζ(3) is an irrational number.
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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.
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Special values of L-functions
In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi, namely by the recognition that expression on the left-hand side is also L(1) where L(s) is the Dirichlet L-function for the Gaussian field.
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Spin wave
Spin waves are propagating disturbances in the ordering of magnetic materials.
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Statistics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.
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Stefan–Boltzmann law
The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature.
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Stieltjes constants
In mathematics, the Stieltjes constants are the numbers \gamma_k that occur in the Laurent series expansion of the Riemann zeta function: The constant \gamma_0.
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Stirling numbers of the first kind
In mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations.
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String theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.
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Theta function
In mathematics, theta functions are special functions of several complex variables.
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Triviality (mathematics)
In mathematics, the adjective trivial is frequently used for objects (for example, groups or topological spaces) that have a very simple structure.
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Umbral calculus
In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to 'prove' them.
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Upper half-plane
In mathematics, the upper half-plane H is the set of complex numbers with positive imaginary part: The term arises from a common visualization of the complex number x + iy as the point (x,y) in the plane endowed with Cartesian coordinates.
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Vinogradov's mean-value theorem
In mathematics, Vinogradov's mean value theorem is an estimate for the number of equal sums of powers.
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Weierstrass factorization theorem
In mathematics, and particularly in the field of complex analysis, the Weierstrass factorization theorem asserts that entire functions can be represented by a product involving their zeroes.
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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.
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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).
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Zeros and poles
In mathematics, a zero of a function is a value such that.
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Zeta function regularization
In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators.
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Zeta function universality
In mathematics, the universality of zeta-functions is the remarkable ability of the Riemann zeta-function and other, similar, functions, such as the Dirichlet L-functions, to approximate arbitrary non-vanishing holomorphic functions arbitrarily well.
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Zipf's law
Zipf's law is an empirical law formulated using mathematical statistics that refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions.
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Zipf–Mandelbrot law
No description.
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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.
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1 + 2 + 3 + 4 + ⋯
The infinite series whose terms are the natural numbers is a divergent series.
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Critical strip, Euler zeta function, Euler-Riemann zeta function, Euler–Riemann zeta function, Reimann Zeta function, Reimann zeta function, Riemann Zeta Function, Riemann Zeta function, Riemann functional equation, Riemann z-function, Riemann zeta, Riemann zeta function zeros, Riemann zeta-function, Riemann ζ-function, Riemann's functional equation, Riemann's zeta function, Riemann-zeta function, Series of reciprocal powers, Trivial zero, Z(s), Ζ(s), Ζ(x).
References
[1] https://en.wikipedia.org/wiki/Riemann_zeta_function
