Related papers: Stuffle product formulas of multiple zeta values
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.
The multiple zeta values (MZVs) possess a rich algebraic structure of algebraic relations, which is conjecturally determined by two different (shuffle and stuffle) products of a certain algebra of noncommutative words. In a recent work,…
In this paper, we formally introduce the notion of Ap{\'e}ry-like sums and we show that every multiple zeta values can be expressed as a $\bf Z$-linear combination of them. We even describe a canonical way to do so. This allows us to put in…
We present a concise method for deriving an explicit formula for $p$-adic multiple zeta values. The formula features a variant of multiple harmonic sums, termed binomial multiple harmonic sums.
In this paper, we study the explicit expressions of multiple t-star values with an arbitrary number of blocks of twos of general level. We give an expression of a generating function of such values, which generalizes the results for…
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…
There has been an avalanche of recent research on multiple zeta values. We propose dividing identities for multiple zeta values into structural and specific types. Structural identities are valid for any generalized multiple zeta function,…
In this paper, we introduce the notion of generalized quasi-shuffle products and give a criterion for their associativity. These extend the quasi-shuffle products introduced by Hoffman, which are often used to describe the stuffle and…
Multiple Dedekind zeta values were recently defined by the second author. In a separate paper, the second author constructed double shuffle relations in some cases as a response to questions asked by Richard Hain and Alexander Goncharov. In…
The sum formula is a well known relation in the field of the multiple zeta values. In this paper, we present its generalization for the Euler-Zagier multiple zeta function.
We prove an easy but interesting result about the linear independence of multiple zeta values of different weights.
The goal of this article is to give an elementary proof of the double shuffle relations directly for the Goncharov and Manin motivic multiple zeta values. The shuffle relation is straightforward, but for the stuffle we use a modification of…
In this paper, we study sum formulas for Schur multiple zeta values and give a generalization of the sum formulas for multiple zeta(-star) values. We show that for ribbons of certain types, the sum over all admissible Young tableaux of this…
The multiple zeta values (MZV) are a set of real numbers with a beautiful structure as an algebra over the rational numbers. They are related to maybe the most important conjecture on mathematics today, the Riemann hypothesis. In this paper…
Multiple q-zeta values are a 1-parameter generalization (in fact, a q-analog) of the multiple harmonic sums commonly referred to as multiple zeta values. These latter are obtained from the multiple q-zeta values in the limit as q tends to…
In this paper we give two idelic representations of the multiple zeta values - one using iterated integrals over the finite ideles and the other using iterated integrals over the idele class group. Each of the representations leads to a…
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…
We show the recurrence relations of the Euler-Zagier multiple zeta-function which describes the $r$-fold function with one variable specialized to a non-positive integer as a rational linear combination of $(r-1)$-fold functions, which…
We show that a duality formula for certain parametrized multiple series yields numerous relations among them. As a result, we obtain a new relation among extended multiple zeta values, which is an extension of Ohno's relation for multiple…
In this paper we introduce and study double tails of multiple zeta values. We show, in particular, that they satisfy certain recurrence relations and deduce from this a generalization of Euler's classical formula…