相关论文: Multiple zeta values over global function fields

In this paper, we generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give…

Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then,…

In this paper, we construct the alternating multiple q-zeta function(= Multiple Euler q-zeta function) and investigate their properties. Finally, we give some interesting functional eauations related to q-Euler polynomials.

In this paper, we systematically investigate the multidimensional $Z$-transform of functions with values in sequentially complete locally convex spaces over the field of complex numbers. We provide many structural characterizations, remarks…

Kaneko and Tsumura introduced a new kind of multiple zeta functions $\eta(k_1,\ldots,k_r;s_1,\ldots,s_r)$. This is an analytic function of complex variables $s_1,\ldots,s_r$, while $k_1,\ldots,k_r$ are non-positive integer parameters. In…

This is the second of four papers that study algebraic and analytic structures associated with the Lerch zeta function. In this paper we analytically continue it as a function of three complex variables. We that it is well defined as a…

We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, respectively.

Using some transformation formulas of the generalized hypergeometric series $\,_3F_2$, we give another proof of D. Zagier's evaluation formula of the multiple zeta values $\zeta(2,...,2,3,2,...,2)$.

We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…

The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…

Inspired by the theory of Hodge correlators due to Goncharov and by the plectic principle of Nekov\'a\v{r} and Scholl, we construct higher plectic Green functions and give a higher order generalization of Hecke's formula for abelian…

We introduce a new type of multiple zeta functions, which we call bilateral zeta functions, analogous to the Barnes zeta functions. The bilateral zeta function is a periodic function and shares certain basic properties of Barnes zeta…

T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an analog of the Arakawa-Kaneko zeta function. One is to find an…

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,…

In this paper, we study multiple zeta values (abbreviated as MZV's) over function fields in positive characteristic. Our main result is to prove Thakur's basis conjecture, which plays the analogue of Hoffman's basis conjecture for real…

In this paper, we study multizeta values over function fields in characteristic $p$. For each $d \geq 2$, we show that when the constant field has cardinality $> 2$, the field generated by all multizeta values of depth $d$ is of infinite…

We study generating functions for multiple zeta star values in general form. These generating functions provide a connection between multiple zeta star values and multiple Euler sums, which allows us to express each multiple zeta star value…

We prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class…

In this paper we shall define a special-valued multiple Hurwitz zeta functions, namely the multiple $t$-values $t(\boldsymbol{\alpha})$ and define similarly the multiple star $t$-values as $t^{\star}(\boldsymbol{\alpha})$. Then we consider…

We study some classical identities for multiple zeta values and show that they still hold for zeta functions built on the zeros of an arbitrary function. We introduce the complementary zeta function of a system, which naturally occurs when…