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Acta Mathematica Hungarica

, Volume 144, Issue 2, pp 515–529 | Cite as

Unified presentation of p-adic L-functions associated with unification of the special numbers

  • H. Ozden
  • Y. SimsekEmail author
Article

Abstract

By using partial differential equations (PDEs) of the generating functions for the unification of the Bernoulli, Euler and Genocchi polynomials and numbers, we derive many new identities and recurrence relations for these polynomials and numbers. In [33], Srivastava et al. defined a unified presentation of certain meromorphic functions related to the families of the partial zeta type functions. By using these functions, we construct p-adic functions which are related to the partial zeta type functions. By applying these p-adic function, we construct unified presentation of p-adic L-functions. These functions give us generalization of the Kubota–Leopoldt p-adic L-functions, which are related to the Bernoulli numbers and the other p-adic L-functions, which are related to the Euler numbers and polynomials. We also give some remarks and comments on these functions.

Key words and phrases

Bernoulli number and polynomial Euler number and polynomial Genocchi number and polynomial Riemann and Hurwitz (or generalized) zeta function partial zeta type function p-adic function p-adic L-function partial differential equation (PDE) generating function 

Mathematics Subject Classification

11B68 11S40 11S80 11M99 30B50 44A05 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2014

Authors and Affiliations

  1. 1.Department of MathematicsFaculty of Art and Science University of UludagBursaTurkey
  2. 2.Department of Mathematics, Faculty of ScienceAkdeniz UniversityAntalyaTurkey

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