Concept information
Preferred term
analytic number theory
Definition(s)
-
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Analytic_number_theory)
Broader concept(s)
Narrower concept(s)
- additive number theory
- Apéry's theorem
- Artin L-function conjecture
- Artin's conjecture on primitive roots
- Barnes G-function
- Bateman-Horn conjecture
- Bernoulli polynomial
- Birch's theorem
- Bombieri-Vinogradov theorem
- Bonse's inequality
- Brauer-Siegel theorem
- Buchstab function
- Chebotarev's density theorem
- Cramér's conjecture
- Degen's eight-square identity
- Dickman function
- Dirichlet density
- divisor function
- Elliott-Halberstam conjecture
- Euler product
- exponential sum
- Gilbreath's conjecture
- Hardy-Littlewood circle method
- Jacobi triple product
- Lambert series
- Legendre's constant
- L-function
- Mahler measure
- modular form
- multiplicative number theory
- Perron's formula
- Porter's constant
- prime-counting function
- prime number
- prime number theorem
- Riemann hypothesis
- Riesel number
- Schinzel's hypothesis H
- second Hardy-Littlewood conjecture
- Sierpiński number
- smooth number
- square-free integer
- Stirling's approximation
- transcendental number theory
- Von Mangoldt function
- Voronoi formula
In other languages
URI
http://data.loterre.fr/ark:/67375/PSR-VHDD6KJX-8
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