ABSTRACT Motivated essentially by recent works by several authors (see, for example, Bin-Saad [Math J Okayama Univ 49:37-52, 2007] and Katsurada [Publ Inst Math (Beograd) (Nouvelle Ser) 62(76):13-25, 1997], the main objective in this paper is to present a systematic investigation of numerous interesting properties of some families of generating functions and their partial sums which are associa...

Let ζ(s1, s2, · · · , sk;α) be the multiple Hurwitz zeta function. Given two positive integers k and n with k 6 n, let E(2n, k;α) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. In this note we present some generating series for the numbers E(2n, k;α).

We study the value-distribution of Hurwitz zeta-function with algebraic irrational parameter $$\zeta (s;\alpha )=\sum _{n\ge _0}(n+\alpha )^{-s}$$ . In particular, we prove effective denseness results and its derivatives in suitable strips containing right boundary critical strip $$1+i{\mathbb {R}}$$ This may be considered as a first “weak” manifestation universality for those zeta-functions.

Abstract. 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 qGenocchi type l-function. Furthermore, we construct new genereting functions of q-Hardy-Berndt type...