UNIFIED PRESENTATION OF p-ADIC L-FUNCTIONS ASSOCIATED WITH UNIFICATION OF THE SPECIAL NUMBERS


Ozden H., Simsek Y.

ACTA MATHEMATICA HUNGARICA, vol.144, no.2, pp.515-529, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 144 Issue: 2
  • Publication Date: 2014
  • Doi Number: 10.1007/s10474-014-0446-9
  • Title of Journal : ACTA MATHEMATICA HUNGARICA
  • Page Numbers: pp.515-529

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.