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A construction of p-adic Hurwitz–Lerch L-function

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Abstract

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

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Acknowledgements

The authors would like to thank anonymous referee for his/her insightful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Akdeniz University, Antalya, 07060, Turkey

    Selin Selen Özbek & Mehmet Cenkci

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  1. Selin Selen Özbek
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  2. Mehmet Cenkci
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Correspondence to Selin Selen Özbek.

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Communicated by Jens Funke.

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Özbek, S.S., Cenkci, M. A construction of p-adic Hurwitz–Lerch L-function. Abh. Math. Semin. Univ. Hambg. 90, 85–98 (2020). https://doi.org/10.1007/s12188-020-00221-z

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  • DOI: https://doi.org/10.1007/s12188-020-00221-z

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