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 |
|---|---|
| URN: | urn:nbn:de:hbz:832-epub4-21307 |
| DOI: | https://doi.org/10.1007/s12188-021-00244-0 |
| ISSN: | 0025-5858 |
| ISSN: | 1865-8784 |
| Parent Title (English): | Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg |
| Publisher: | Springer Berlin Heidelberg |
| Document Type: | Article |
| Language: | English |
| 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 |
| Volume: | 91 |
| Issue: | 2 |
| 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 |
| DeepGreen: | DeepGreen |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |