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Concept information

mathematical analysis > calculus > series > Dirichlet series > Dirichlet L-series
... > number > number theory > analytic number theory > L-function > Dirichlet series > Dirichlet L-series
... > mathematical analysis > complex analysis > meromorphic function > L-function > Dirichlet series > Dirichlet L-series

Terme préférentiel

Dirichlet L-series  

Définition

  • In mathematics, a Dirichlet L-series is a function of the form


    where is a Dirichlet character and s a complex variable with real part greater than 1. It is a special case of a Dirichlet series. By analytic continuation, it can be extended to a meromorphic function on the whole complex plane, and is then called a Dirichlet L-function and also denoted L(s, χ).
    These functions are named after Peter Gustav Lejeune Dirichlet who introduced them in (Dirichlet 1837) to prove the theorem on primes in arithmetic progressions that also bears his name. In the course of the proof, Dirichlet shows that L(s, χ) is non-zero at s = 1. Moreover, if χ is principal, then the corresponding Dirichlet L-function has a simple pole at s = 1. Otherwise, the L-function is entire.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Dirichlet_L-function)

Concept générique

Concepts spécifiques

Synonyme(s)

  • Dirichlet L-function

Traductions

URI

http://data.loterre.fr/ark:/67375/PSR-XQZPCT5B-R

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RDF/XML TURTLE JSON-LD Date de création 04/08/2023, dernière modification le 04/08/2023