Category:Analytic number theory

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Analytic number theory is the branch of number theory that uses methods from mathematical analysis. Its first major success was the application of complex analysis in the proofs of the prime number theorem based on the Riemann zeta function.

Subcategories

This category has the following 3 subcategories, out of 3 total.

Pages in category "Analytic number theory"

The following 79 pages are in this category, out of 79 total. This list may sometimes be slightly out of date (learn more)

A

Abstract analytic number theory
Analytic number theory
Apéry's constant
Artin conjecture
Artin's conjecture on primitive roots

B

Bateman-Horn conjecture
Birch's theorem
Bombieri–Friedlander–Iwaniec theorem
Bombieri–Vinogradov theorem
Brauer-Siegel theorem
Brun sieve
Brun's constant
Brun's theorem
Brun–Titchmarsh theorem

C

Character sum
Chebotarev's density theorem
Chen's theorem
Classical modular curve
Constant problem
Cramér's conjecture
Critical line theorem

D

De Bruijn-Newman constant
Degen's eight-square identity
Dickman-de Bruijn function
Dirichlet density

E

Effective results in number theory

E cont.

Eisenstein series
Elliott–Halberstam conjecture
Elliptic curve
Elliptic function
Euler's four-square identity
Exponential sum

F

Fermat polygonal number theorem
Fundamental lemma of sieve theory

G

Gilbreath's conjecture
Goldbach's conjecture
Goldbach's weak conjecture
Green–Tao theorem

H

Hardy–Littlewood circle method
Hardy–Ramanujan theorem
Hua's lemma

K

Kloosterman sum
Kronecker limit formula

L

Lagrange's four-square theorem
Lambert series
Landau prime ideal theorem
Landau–Ramanujan constant
Large sieve
Legendre sieve
Linnik's theorem

M

Mahler measure
Modular form
Modular group

M cont.

The Music of the Primes

O

Odlyzko-Schönhage algorithm
On the Number of Primes Less Than a Given Magnitude

P

Parity problem (sieve theory)
Perron's formula
Prime number theorem
Prime-counting function

R

Real analytic Eisenstein series
Riemann hypothesis
Riemann-von Mangoldt formula
Riesel number

S

Schinzel's hypothesis H
Schnirelmann density
Second Hardy-Littlewood conjecture
Selberg sieve
Seventeen or Bust
Siegel–Walfisz theorem
Sieve theory
Smooth number
Stirling's approximation

T

Transcendence theory
Turán sieve
Twin prime conjecture

U

User:SofaKid/Sandbox

V

Vaughan's identity

W

Waring's problem

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