"Riemann zeta function" meaning in English

See Riemann zeta function in All languages combined, or Wiktionary

Noun

Forms: Riemann zeta functions [plural]
Etymology: Named after German mathematician Bernhard Riemann. Etymology templates: {{named-after/list|mathematician||||}} mathematician, {{!}} |, {{lang|en|Bernhard Riemann}} Bernhard Riemann, {{named-after|en|Bernhard Riemann|nationality=German|occupation=mathematician|wplink=Bernhard Riemann}} Named after German mathematician Bernhard Riemann Head templates: {{en-noun|-|s}} Riemann zeta function (usually uncountable, plural Riemann zeta functions)
  1. (number theory, analytic number theory, uncountable) The function ζ defined by the Dirichlet series ζ(s)=∑ₙ₌₁ ᪲1/(nˢ)=1/(1ˢ)+1/(2ˢ)+1/(3ˢ)+1/(4ˢ)+⋯, which is summable for points s in the complex half-plane with real part > 1; the analytic continuation of said function, being a holomorphic function defined on the complex numbers with pole at 1. Tags: uncountable, usually Categories (topical): Functions, Number theory Synonyms (analytic continuation of a function defined as the sum of a Dirichlet series): Euler–Riemann zeta function Hypernyms (analytic continuation of a function defined as the sum of a Dirichlet series): analytic function, zeta function Translations (analytic continuation of a function defined as the sum of a Dirichlet series): Riemann-zeta-functie (Dutch), riemannsche ζ-Funktion [feminine] (German), funzione zeta di Riemann [feminine] (Italian), función zeta de Riemann [feminine] (Spanish), Riemann zeta fonksiyonu (Turkish)
    Sense id: en-Riemann_zeta_function-en-noun-b2kk8DNd Topics: analytic-number-theory, mathematics, number-theory, sciences Disambiguation of 'analytic continuation of a function defined as the sum of a Dirichlet series': 83 17 Disambiguation of 'analytic continuation of a function defined as the sum of a Dirichlet series': 82 18 Disambiguation of 'analytic continuation of a function defined as the sum of a Dirichlet series': 83 17
  2. (countable) A usage of (a specified value of) the Riemann zeta function, such as in an equation. Tags: countable, usually Synonyms: Riemann zeta-function, Riemann's zeta function Related terms: Dirichlet eta function, Dirichlet series, L-function, L-series, Riemann hypothesis, zeta function
    Sense id: en-Riemann_zeta_function-en-noun-5VW9AkJs Categories (other): English entries with incorrect language header, English entries with topic categories using raw markup, English terms with non-redundant non-automated sortkeys Disambiguation of English entries with incorrect language header: 45 55 Disambiguation of English entries with topic categories using raw markup: 36 64 Disambiguation of English terms with non-redundant non-automated sortkeys: 40 60

Inflected forms

Alternative forms

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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-05 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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