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Yilmaz Simsek

Publications and source records attributed to Yilmaz Simsek.

41 records · Page 3Linked to original sources
arXiv2007

On q-deformed Stirling numbers

The purpose of this article is to introduce q-deformed Stirling numbers of the first and second kinds. Relations between these numbers, Riemann zeta function and q-Bernoulli numbers of higher order are given. Some relations related to the classical Stirling numbers and Bernoulli numbers of higher order are found. By using derivative operator to the generating function of the q-deformed Stirling numbers of the second kinds, a new function is defined which interpolates the q-deformed Stirling numbers of the second kinds at negative integers. The recurrence relations of the Stirling numbers of the first and second kind are given. In addition, relation between q-deformed Stirling numbers and q-Bell numbers is obtained.

math.NT↗
arXiv2007

Twisted p-adic (h,q)-L-functions

By using q-Volkenborn integral on Z_{p}, we (simsek, simsekCanada) constructed new generating functions of the (h,q)-Bernoulli polynomials and numbers. By applying the Mellin transformation to the generating functions, we constructed integral representation of the twisted (h,q)-Hurwitz function and twisted (h,q)-two-variable L-function. By using these functions, we construct twisted new (h,q)-partial zeta function which interpolates the twisted (h,q)-Bernoulli polynomials and generalized twisted (h,q)-Bernoulli numbers at negative integers. We give relation between twisted (h,q)-partial zeta functions and twisted (h,q)-two-variable L-function. We find the value of this function at s=0. We also find residue of this function at s=1. We construct p-adic twisted (h,q)-L-function, which interpolates the twisted (h,q)-Bernoulli polynomials.

math.NT↗
arXiv2007

q-Hardy-Berndt type sums associated with q-Genocchi type zeta and l-functions

The aim of this paper is to define new generating functions. By applying the Mellin transformation formula to these generating functions, we define q-analogue of Genocchi zeta function, q-analogue Hurwitz type Genocchi zeta function, q-analogue Genocchi type l-function and two-variable q-Genocchi type l-function. Furthermore, we construct new genereting functions of q-Hardy-Berndt type sums and q-Hardy-Berndt type sums attached to Dirichlet character. We also give some new relations related to q-Hardy-Berndt type sums and q-Genocchi zeta function as well.

math.NT↗