Back نظرية الأعداد التحليلية Arabic Teoría analítica de númberos AST Аналитична теория на числата Bulgarian বিশ্লেষণী সংখ্যাতত্ত্ব Bengali/Bangla Teoria analítica de nombres Catalan Analytische Zahlentheorie German Αναλυτική θεωρία αριθμών Greek Teoría analítica de números Spanish Zenbakien teoria analitikoa Basque نظریه تحلیلی اعداد Persian

Analytic number theory

Riemann zeta function ζ(s) in the complex plane. The color of a point s encodes the value of ζ(s): colors close to black denote values close to zero, while hue encodes the value's argument.

In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.[1] 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.[1][2] 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).

  1. ^ a b Apostol 1976, p. 7.
  2. ^ Davenport 2000, p. 1.

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