Related papers: Some evaluations of interpolated multiple zeta val…
We study rather general multiple zeta-functions whose denominators are given by polynomials. The main aim is to prove explicit formulas for the values of those multiple zeta-functions at non-positive integer points. We first treat the case…
We prove a new class of relations among multiple zeta values (MZV's) which contains Ohno's relation. We also give the formula for the maximal number of independent MZV's of fixed weight, under our new relations. To derive our formula for…
The sum formula is one of the most well-known relations among multiple zeta values. This paper proves a conjecture of Kaneko predicting that an analogous formula holds for finite multiple zeta values.
We treat interpolation for various logics.
We study an elliptic analogue of multiple zeta values, the elliptic multiple zeta values of Enriquez, which are the coefficients of the elliptic KZB associator. Originally defined by iterated integrals on a once-punctured complex elliptic…
This survey article is the written version of two talks given at the Journ\'ees X-UPS 2019 "P\'eriodes et transcendance" at \'Ecole polytechnique. We give a gentle introduction to the study of multiple zeta values, from Euler's solution to…
In this paper, we settle the problem posed by Singer which is on a comparison problem between the renormalized values of shuffle type and of harmonic type of multiple zeta functions.
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 present a formula for the interpolation of matrix weighted spaces of vector valued functions via interpolation functors. We apply our formula to the particular case of interpolation of matrix weighted $L^p$ spaces by the real and complex…
In this paper we present some new identities for multiple polylogarithms (abbr. MPLs) and multiple harmonic star sums (abbr. MHSSs) by using the methods of iterated integral computations of logarithm functions. Then, by applying these…
We know at least two ways to generalize multiple zeta(-star) values, or MZ(S)Vs for short, which are $q$-analogue and $t$-interpolation. The $q$-analogue of MZ(S)Vs, or $q$MZ(S)Vs for short, was introduced by Bradley, Okuda and Takeyama,…
In this paper, we establish some new identities of integrals involving multiple polylogarithm functions and their level two analogues in terms of Hurwitz-type multiple zeta (star) values. Using these identities, we provide new proofs of the…
It is shown that novel relations between multiple zeta values and single-variable multiple polylogarithms at 1/2 (delta values) can be derived by comparing two distinct, yet a priori equal, series formulae for the Drinfeld associator (from…
In this paper we present some of the recent progresses in multiple zeta values (MZVs). We review the double shuffle relations for convergent MZVs and summarize generalizations of the sum formula and the decomposition formula of Euler for…
Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted…
For $k\leq n$, let $E(mn,k)$ be the sum of all multiple zeta values of depth $k$ and weight $mn$ with arguments are multiples of $m\geq 2$. More precisely, $E(mn,k)=\sum_{|\boldsymbol{\alpha}|=n}\zeta(m\alpha_1,m\alpha_2,\ldots,…
We explicitly evaluate a special type of multiple Dirichlet $L$-values at positive integers in two different ways: One approach involves using symmetric functions, while the other involves using a generating function of the values. Equating…
In this note, we shall discuss a generalization of Thakur's multiple zeta values and allied objects, in the framework of function fields of positive characteristic and more precisely, of periods in Tate algebras.
The sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values bear a striking resemblance. We explain the resemblance in a rather straightforward manner using an identity that involves the Schur multiple zeta…
Five series are evaluated in terms of zeta values. Three of the series involve harmonic numbers and one involves Stirling numbers of the first kind. The evaluation of these series is reduced to the evaluation of certain integrals, including…