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Number theory and Riemann hypothesis

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Number theory and Riemann hypothesis

Number theory vs. Riemann hypothesis

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers. 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.

Similarities between Number theory and Riemann hypothesis

Number theory and Riemann hypothesis have 23 things in common (in Unionpedia): Algebraic number field, Algebraic variety, American Mathematical Society, Automorphic form, Complex analysis, Cramér's conjecture, Dedekind zeta function, Disquisitiones Arithmeticae, Elliptic curve, Finite field, G. H. Hardy, Goldbach's conjecture, Group theory, Iwasawa theory, John Wiley & Sons, L-function, Leonhard Euler, Primality test, Prime number, Prime number theorem, Pure mathematics, Real number, Riemann zeta function.

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.

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Algebraic variety

Algebraic varieties are the central objects of study in algebraic geometry.

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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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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.

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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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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.

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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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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.

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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.

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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.

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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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Goldbach's conjecture

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics.

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Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

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Iwasawa theory

In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields.

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John Wiley & Sons

John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.

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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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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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Primality test

A primality test is an algorithm for determining whether an input number is prime.

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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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Pure mathematics

Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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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.

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The list above answers the following questions

Number theory and Riemann hypothesis Comparison

Number theory has 216 relations, while Riemann hypothesis has 185. As they have in common 23, the Jaccard index is 5.74% = 23 / (216 + 185).

References

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