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...

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

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

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...

undergraduate in mathematics. 1995 Winner: Kannan Soundararajan (Analytic Number Theory, University of Michigan) Honorable mention: Kiran Kedlaya (Harvard...

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

functions and other formulas in the fields of probability, statistics, analytic number theory, and combinatorics. The gamma function can be seen as a solution...

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

additive functions and the DDT theorem. Number theory Analytic number theory Areas of mathematics List of number theory topics List of probability topics Probabilistic...

was a Soviet mathematician, who was one of the creators of modern analytic number theory, and also a dominant figure in mathematics in the USSR. He was born...

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

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

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...

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...

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...

In mathematics, and more particularly in analytic number theory, Perron's formula is a formula due to Oskar Perron to calculate the sum of an arithmetic...

computability is reflected in and contrasts with the approach used in the analytic number theory to prove the results. It for example brings into question any use...

Academy of Sciences. He has made important contributions to analytic and algebraic number theory as well as harmonic analysis. He is the recipient of Cole...

(born 1944) is an American mathematician, working in the fields of analytic number theory and mathematical analysis. He is the namesake of Montgomery's pair...

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

Heath-Brown is a British mathematician working in the field of analytic number theory. He was an undergraduate and graduate student of Trinity College...

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

area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having...

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

Fields Medal for his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory. He is the second Australian and the...

run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference...

discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential...

of Lie theory. The compact case arises through Euler's formula in the complex plane. Other one-parameter groups occur in the split-complex number plane...