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- Riemann_zeta_function abstract "The Riemann zeta function or Euler–Riemann zeta function, ζ(s), is a function of a complex variable s that analytically continues the sum of the infinite series , which converges when the real part of s is greater than 1. More general representations of ζ(s) for all s are given below. The Riemann zeta function plays a pivotal role in analytic number theory and has applications in physics, probability theory, and applied statistics.This function, as a function of a real argument, was introduced and studied by Leonhard Euler in the first half of the eighteenth century without using complex analysis, which was not available at that time. Bernhard Riemann in his article "On the Number of Primes Less Than a Given Magnitude" published in 1859 extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation and established a relation between its zeros and the distribution of prime numbers.The values of the Riemann zeta function at even positive integers were computed by Euler. The first of them, ζ(2), provides a solution to the Basel problem. In 1979 Apéry proved the irrationality of ζ(3). The values at negative integer points, also found by Euler, are rational numbers and play an important role in the theory of modular forms. Many generalizations of the Riemann zeta function, such as Dirichlet series, Dirichlet L-functions and L-functions, are known.".
- Riemann_zeta_function thumbnail Complex_zeta.jpg?width=300.
- Riemann_zeta_function wikiPageExternalLink 0309433v1.
- Riemann_zeta_function wikiPageExternalLink zeta_tables.
- Riemann_zeta_function wikiPageExternalLink Zeta.
- Riemann_zeta_function wikiPageExternalLink RiemannZetaFunction.html.
- Riemann_zeta_function wikiPageExternalLink prime_numbers_get_hitched.php.
- Riemann_zeta_function wikiPageExternalLink page_807.htm.
- Riemann_zeta_function wikiPageExternalLink watch?v=MsBUTuYI62k.
- Riemann_zeta_function wikiPageID "25809".
- Riemann_zeta_function wikiPageRevisionID "605719198".
- Riemann_zeta_function first "T. M.".
- Riemann_zeta_function hasPhotoCollection Riemann_zeta_function.
- Riemann_zeta_function id "25".
- Riemann_zeta_function id "p/z099260".
- Riemann_zeta_function last "Apostol".
- Riemann_zeta_function title "Zeta and Related Functions".
- Riemann_zeta_function title "Zeta-function".
- Riemann_zeta_function subject Category:Analytic_number_theory.
- Riemann_zeta_function subject Category:Meromorphic_functions.
- Riemann_zeta_function subject Category:Zeta_and_L-functions.
- Riemann_zeta_function type Abstraction100002137.
- Riemann_zeta_function type Function113783816.
- Riemann_zeta_function type MathematicalRelation113783581.
- Riemann_zeta_function type MeromorphicFunctions.
- Riemann_zeta_function type Relation100031921.
- Riemann_zeta_function comment "The Riemann zeta function or Euler–Riemann zeta function, ζ(s), is a function of a complex variable s that analytically continues the sum of the infinite series , which converges when the real part of s is greater than 1. More general representations of ζ(s) for all s are given below.".
- Riemann_zeta_function label "Fonction zêta de Riemann".
- Riemann_zeta_function label "Función zeta de Riemann".
- Riemann_zeta_function label "Funkcja dzeta Riemanna".
- Riemann_zeta_function label "Funzione zeta di Riemann".
- Riemann_zeta_function label "Função zeta de Riemann".
- Riemann_zeta_function label "Riemann zeta function".
- Riemann_zeta_function label "Riemann-zèta-functie".
- Riemann_zeta_function label "Riemannsche ζ-Funktion".
- Riemann_zeta_function label "Дзета-функция Римана".
- Riemann_zeta_function label "دالة زيتا لريمان".
- Riemann_zeta_function label "リーマンゼータ関数".
- Riemann_zeta_function label "黎曼ζ函數".
- Riemann_zeta_function sameAs Riemannova_funkce_zeta.
- Riemann_zeta_function sameAs Riemannsche_ζ-Funktion.
- Riemann_zeta_function sameAs Συνάρτηση_ζήτα.
- Riemann_zeta_function sameAs Función_zeta_de_Riemann.
- Riemann_zeta_function sameAs Fonction_zêta_de_Riemann.
- Riemann_zeta_function sameAs Fungsi_zeta_Riemann.
- Riemann_zeta_function sameAs Funzione_zeta_di_Riemann.
- Riemann_zeta_function sameAs リーマンゼータ関数.
- Riemann_zeta_function sameAs 리만_제타_함수.
- Riemann_zeta_function sameAs Riemann-zèta-functie.
- Riemann_zeta_function sameAs Funkcja_dzeta_Riemanna.
- Riemann_zeta_function sameAs Função_zeta_de_Riemann.
- Riemann_zeta_function sameAs m.06fp7.
- Riemann_zeta_function sameAs Q187235.
- Riemann_zeta_function sameAs Q187235.
- Riemann_zeta_function sameAs Riemann_zeta_function.
- Riemann_zeta_function wasDerivedFrom Riemann_zeta_function?oldid=605719198.
- Riemann_zeta_function depiction Complex_zeta.jpg.
- Riemann_zeta_function isPrimaryTopicOf Riemann_zeta_function.