Related papers: Barnes' type multiple Changhee q-zeta functiond
Previously the authors proved subconvexity of Shintani's zeta function enumerating class numbers of binary cubic forms. Here we return to prove subconvexity of the Maass form twisted version.
Ohno's relation gives a large family of relations of the multiple zeta values. We shall show functional relations of generating functions of Ohno's relation. With these relations we present a new proof of Ohno's relation.
In this paper, we give a simple proof of the functional relation for the Lerch type Tornheim double zeta function. By using it, we obtain simple proofs of some explicit evaluation formulas for double $L$-values.
The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.
In this paper, we give a formula that connects two variants of multiple zeta values; multitangent functions and symmetric multiple zeta values. As an application of this formula, we give two results. First, we prove Bouillot's conjecture on…
We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.
In this paper, we consider Barnes-type Daehee polynomials of the first kind and of the second kind. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.
We study the Hurwitz-type analogue of Schur multiple zeta-functions involving shifting parameters. We extend various formulas, known for ordinary Schur multiple zeta-functions, to the case of Hurwitz type. We also mention unpublished…
We obtain a class of quadratic relations for a q-analogue of multiple zeta values (qMZV's). In the limit q->1, it turns into Kawashima's relation for multiple zeta values. As a corollary we find that qMZV's satisfy the linear relation…
Using the Jackson integral, we obtain the $q$-integral analogue of the Raabe type formulas for Barnes multiple Hurwitz-Lerch zeta functions and Barnes and Vardi's multiple gamma functions. Our results generalize $q$-integral analogue of the…
In this paper, a new construction of quaternary bent functions from quaternary quadratic forms over Galois rings of characteristic 4 is proposed. Based on this construction, several new classes of quaternary bent functions are obtained, and…
We introduce two types bilateral zeta functions, which are related to the primitive and normalized multiple sine functions respectively. Further, we establish their main properties, that is, Fourier expansions, analytic continuations,…
This note contains a short proof of the functional equation for the zeta function.
The main object of this paper is to construct a new generating function of the (q-) Bernstein type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and…
In the former part of this paper, we give functional equations for Barnes multiple zeta-functions and consider some relevant results. In particular, we show that Ramanujan's classical formula for the Riemann zeta values can be derived from…
This work is an example driven overview article of recent works on the connection of multiple zeta values, modular forms and q-analogues of multiple zeta values given by multiple Eisenstein series.
We survey various results and conjectures concerning multiple polylogarithms and the multiple zeta function. Among the results, we announce our resolution of several conjectures on multiple zeta values. We also provide a new integral…
We construct the q-twisted cohomology associated with the q-multiplicative function of Jordan-Pochhammer type at |q|=1. In this framework, we prove the Heine's relations and a connection formula for the q-hypergeometric function of the…
The present paper deals with the q-analogue of Bernstein, Meyer-Konig-Zeller and Beta operators. Here we estimate the generating functions for q-Bernstein, q-Meyer-Konig-Zeller and q-Beta basis 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,…