Related papers: A continuous version of multiple zeta values with …

We introduce the method of desingularization of multi-variable multiple zeta-functions (of the generalized Euler-Zagier type), under the motivation of finding suitable rigorous meaning of the values of multiple zeta-functions at…

We establish the meromorphic continuation of certain multiple zeta functions of generalized Hurwitz type. From this meromorphic continuation, we obtain explicit formulas for their (derivative) values at nonpositive integers along a given…

In recent years, a variety of variants of multiple zeta values (MZVs) have been defined and studied. One way to produce these variants is to restrict the indices in the definition of MZVs to some fixed parity pattern, which include…

This paper contains examples of shuffle relations among multiple Dedekind zeta values. Dedekind zeta values were defined by the author in his paper "Multiple Dedekind zeta functions". Here we concentrate on the cases of real or imaginary…

The aim of this work is to study the analytic continuation of the doubly-periodic Barnes zeta function. By using a suitable complex integral representation as a starting point we find the meromorphic extension of the doubly periodic Barnes…

This note is a compilation of related research on modular relations for multiple zeta values. Roughly speaking, modular relations are (homogeneous) linear relations of multiple zeta values of fixed weight whose coefficients are `originated'…

It is known that there are infinitely many singularities of multiple zeta functions and the special values at non-positive integer points are indeterminate. In order to give a suitable rigorous meaning of the special values there, Furusho,…

In this paper we define multiple Dedekind zeta values (MDZV), using a new type of iterated integrals, called iterated integrals on a membrane. One should consider MDZV as a number theoretic generalization of Euler's multiple zeta values.…

We prove three theorems on finite real multiple zeta values: the symmetric formula, the sum formula and the height-one duality theorem. These are analogues of their counterparts on finite multiple zeta values.

We study a certain class of q-analogues of multiple zeta values, which appear in the Fourier expansion of multiple Eisenstein series. Studying their algebraic structure and their derivatives we propose conjectured explicit formulas for the…

Denote by $\epsilon$ a primitive root of $N^{th}$-unity. In this paper, we show that the unit cyclotomic multiple zeta values for $\mu_N$ generate all the cyclotomic multiple zeta values for $\mu_N$ in cases $N=2,3,4$. Moreover, the unit…

We define finite multiple zeta values (FMZVs) associated with some combinatorial objects, which we call 2-colored rooted trees, and prove that FMZVs associated with 2-colored rooted trees satisfying certain mild assumptions can be written…

We define the interpolated polynomial multiple zeta values as a generalization of all of multiple zeta values, multiple zeta-star values, interpolated multiple zeta values, symmetric multiple zeta values, and polynomial multiple zeta…

Let $r\ge 1$ be an integer. For any multiple index $\mathbf{s}=(s_1,s_2,\cdots,s_r) \in\mathbb{Z}_{\geq 1}^r$ with $s_r>1$, the multiple zeta value (MZV for short) is defined by \begin{align*} \zeta(s_1,s_2,\cdots,s_r):=\sum_{1\leq…

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 article, we derive meromorphic continuation of multiple Lerch zeta functions by generalising an elegant identity of Ramanujan. Further, we describe the set of all possible singularities of these functions. Finally, for the multiple…

We introduce a symbolic representation of $r$-fold harmonic sums at negative indices. This representation allows us to recover and extend some recent results by Duchamp et al., such as recurrence relations and generating functions for these…

In this paper, we explain several conjectures about how a product of two Carlitz-Goss zeta values can be expressed as a F_p-linear combination of Thakur's multizeta values, generalizing the q=2 case dealt by D. Thakur in Relations between…

We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in…

Multiple zeta values are real numbers defined by an infinite series generalizing values of the Riemann zeta function at positive integers. Finite truncations of this series are called multiple harmonic sums and are known to have interesting…