A Note on Regularized Bernoulli Distributions and P-Adic Dirichlet Expansions
In: De.arXiv.org (2020)
2020Essay / Article in JournalOpen Access
Faculty of Information, Media and Electrical Engineering » Institute of Communication Systems
Title:
A Note on Regularized Bernoulli Distributions and P-Adic Dirichlet Expansions
Creator:
Knospe, HeikoTH Köln
- DHSB-ID
- THK0001442
- SCOPUS
- 6507866242
- Other
- person connected with TH Köln
Author:
Knospe, HeikoTH Köln
- DHSB-ID
- THK0001442
- SCOPUS
- 6507866242
- Other
- person connected with TH Köln
Year of publication:
2020
„Publication Channel“:
Open Access
arXiv.org ID
WWW URL:
Language of text:
English
Type of resource:
Text
Access Rights:
open access
Peer Reviewed:
Not Peer Reviewed
Practice Partner:
No
Category:
Research
Part of statistic:
Part of statistic
Abstract:
We consider Bernoulli distributions and their regularizations, which are measures on the p-adic integers Zp. It is well known that their Mellin transform can be used to define p-adic L-functions. We show that for p>2 one of the regularized Bernoulli distributions is particularly simple and equal to a measure on Zp that takes the values ±1/2 on clopen balls. We apply this to to p-adic L-functions for Dirichlet characters of p-power conductor and obtain Dirichlet series expansions similar to the complex case. Such expansions were studied by D. Delbourgo, and this contribution provides an approach via p-adic measures.