In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers...

properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation...

Abstract analytic number theory is a branch of mathematics which takes the ideas and techniques of classical analytic number theory and applies them to...

Abstract analytic number theory, the application of ideas and techniques from analytic number theory to other mathematical fields Analytic combinatorics...

analytic Eisenstein series is a special function of two variables. It is used in the representation theory of SL(2,R) and in analytic number theory....

Multiplicative number theory is a subfield of analytic number theory that deals with prime numbers and with factorization and divisors. The focus is usually...

largest proper divisor of n can be no larger than ⁠n/2⁠. Abstract analytic number theory for information about generalizations of the theorem. Landau prime...

in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics,...

Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation...

Erdős–Kac theorem on additive functions. Number theory Analytic number theory Areas of mathematics List of number theory topics List of probability topics Probabilistic...

study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the...

June 1987) is an English mathematician working in analytic number theory and in particular the theory of prime numbers. In 2017, he was appointed Research...

In analytic number theory, the Siegel–Walfisz theorem was obtained by Arnold Walfisz as an application of a theorem by Carl Ludwig Siegel to primes in...

by either analytic methods such as Liouville's theorem, or topological ones such as the winding number, or a proof combining Galois theory and the fact...

combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory. Tao was born to Chinese immigrant parents and raised...

gegebenen Größe" ("On the Number of Primes Less Than a Given Magnitude"), one of the milestones in the development of analytic number theory—the branch of mathematics...

certainly useful in applications. A large part of twentieth century analytic number theory was devoted to finding good estimates for these sums, a trend started...

questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several...

In analytic number theory, the Dickman function or Dickman–de Bruijn function ρ is a special function used to estimate the proportion of smooth numbers...

generalizations. The theory of L-functions has become a very substantial, and still largely conjectural, part of contemporary analytic number theory. In it, broad...

was a Czech-born British mathematician, working in the field of analytic number theory. He is remembered in part for the Elliott–Halberstam conjecture...

holomorphic modular newform." Jacob Tsimerman – "For outstanding work in analytic number theory and arithmetic geometry, including breakthroughs on the André–Oort...

transliterated Moebius) in 1832. It is ubiquitous in elementary and analytic number theory and most often appears as part of its namesake the Möbius inversion...

list of number theory topics. See also: List of recreational number theory topics Topics in cryptography Composite number Highly composite number Even and...

application of powerful analytic methods; all of these have become essential concepts and tools of modern analytic number theory. Among the new definitions...

the Riemann hypothesis, is regarded as a foundational paper of analytic number theory. Through his pioneering contributions to differential geometry,...

principle in functional analysis, used in large sieve method of analytic number theory Wave–particle duality Duality (mathematics) Duality (disambiguation)...

Johnson–Lindenstrauss lemma (Euclidean geometry) Margulis lemma Lebesgue's number lemma (dimension theory) Gauss's lemma (Riemannian geometry) Craig interpolation lemma...

In analytic number theory, the Brun–Titchmarsh theorem, named after Viggo Brun and Edward Charles Titchmarsh, is an upper bound on the distribution of...

value one, or square integral one, depending on the application. In number theory, 1 is the value of Legendre's constant, introduced in 1808 by Adrien-Marie...