TY  - JOUR
U1  - Zeitschriftenartikel, wissenschaftlich - begutachtet (reviewed)
A1  - Knospe, Heiko
A1  - Washington, Lawrence C.
T1  - Dirichlet series expansions of p-adic L-functions
JF  - Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
N2  - 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.
KW  - p-adic L-Functions
KW  - Dirichlet Characters
KW  - Dirichlet Series
KW  - Euler Factors
KW  - Regularized Bernoulli Distributions
KW  - p-adic Measures
KW  - Primary: 11R23
KW  - Secondary: 11R42
KW  - 11S80
KW  - 11M41
Y1  - 2021
UN  - https://nbn-resolving.org/urn:nbn:de:hbz:832-epub4-21307
SN  - 0025-5858
SS  - 0025-5858
SN  - 1865-8784
SS  - 1865-8784
U6  - https://doi.org/10.1007/s12188-021-00244-0
DO  - https://doi.org/10.1007/s12188-021-00244-0
VL  - 91
IS  - 2
SP  - 325
EP  - 334
S1  - 10
PB  - Springer Berlin Heidelberg
ER  -