A construction ofp-adic Hurwitz-LerchL-function

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Ozbek S. S., CENKCİ M.

ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, vol.90, no.1, pp.85-98, 2020 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 90 Issue: 1
• Publication Date: 2020
• Doi Number: 10.1007/s12188-020-00221-z
• Journal Name: ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet
• Page Numbers: pp.85-98
• Keywords: p-adicL-function, p-adic Hurwitz-LerchL-function, Kummer congruences, ZETA
• Akdeniz University Affiliated: Yes

Abstract

We derive the existence ofp-adic Hurwitz-LerchL-function by means of a method provided by Washington. This function is a generalization of the one-variablep-adicL-function of Kubota and Leopoldt, and two-variablep-adicL-function of Fox. We also deduce divisibility properties of generalized Apostol-Bernoulli polynomials, in particular establish Kummer-type congruences for them.