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Dirichlet series expansions of p-adic L-functions

  • We study p-adic L-functions Lp(s, 휒) for Dirichlet characters 휒. We show that Lp(s, 휒) has a Dirichlet series expansion for each regularization parameter c that is prime to p and the conductor of 휒. The expansion is proved by transforming a known formula for p-adic L-functions and by controlling the limiting behavior. A fnite number of Euler factors can be factored of in a natural manner from the p-adic Dirichlet series. We also provide an alternative proof of the expansion using p-adic measures and give an explicit formula for the values of the regularized Bernoulli distribution. The result is particularly simple for c = 2, where we obtain a Dirichlet series expansion that is similar to the complex case.

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Author:Heiko Knospe, Lawrence C. Washington
Parent Title (English):Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
Publisher:Springer Berlin Heidelberg
Document Type:Article
Date of first Publication:2021/10/01
Date of Publication (online):2023/04/25
Tag:11M41; 11S80; Dirichlet Characters; Dirichlet Series; Euler Factors; Primary: 11R23; Regularized Bernoulli Distributions; Secondary: 11R42; p-adic L-Functions; p-adic Measures
Page Number:10
Institutes:Informations-, Medien- und Elektrotechnik (F07) / Fakultät 07 / Institut für Nachrichtentechnik
Dewey Decimal Classification:500 Naturwissenschaften und Mathematik
Open Access:Open Access
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International