ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 2, 2008, pp.435-453
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.2.435

Title & Authors

ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS

Kim, Tae-Kyun; Rim, Seog-Hoon; Simsek, Yilmaz; Kim, Dae-Yeoul;

Kim, Tae-Kyun; Rim, Seog-Hoon; Simsek, Yilmaz; Kim, Dae-Yeoul;

Abstract

In this paper, by using q-deformed bosonic p-adic integral, we give -Bernoulli numbers and polynomials, we prove Witt`s type formula of -Bernoulli polynomials and Gauss multiplicative formula for -Bernoulli polynomials. By using derivative operator to the generating functions of -Bernoulli polynomials and generalized -Bernoulli numbers, we give Hurwitz type -zeta functions and Dirichlet`s type -L-functions; which are interpolated -Bernoulli polynomials and generalized -Bernoulli numbers, respectively. We give generating function of -Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and -Bernoulli polynomials and ordinary Bernoulli numbers of order r and -Bernoulli numbers, respectively. We also study on -Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define -partial zeta function and interpolation function.

Keywords

Bernoulli numbers and polynomials;zeta functions;

Language

English

Cited by

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Unification of Multiple Lerch-Zeta Type Functions,;;

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3.

INTERPOLATION FUNCTIONS OF THE EULERIAN TYPE POLYNOMIALS AND NUMBERS,;

Advanced Studies in Contemporary Mathematics, 2013. vol.23. 2, pp.301-307

4.

A formula for generating modular forms with weight 4,;

5.

APOSTOL TYPE DAEHEE NUMBERS AND POLYNOMIALS,;

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