Related papers: Algebraic setup of non-strict multiple zeta values

We exhibit the double q-shuffle structure for the qMZVs recently introduced by Y. Ohno, J. Okuda and W. Zudilin.

This paper aims to study the zero distribution of $v-$adic multiple zeta values over function fields. We show that the interpolated $v-$adic MZVs at negative integers only vanish at what we call the ''trivial zeros'', for degree one prime…

In this paper, we provide an alternative method to calculate the values of generalized multiple Hurwitz zeta function at non-positive integers by means of \emph{Raabe}'s formula and the \textit{Bernoulli} numbers.

We provide a proof of a conjecture by Zhao concerning the structure of certain relations among cyclotomic multiple zeta values in weight two. We formulate this conjecture in a broader algebraic setting in which we give a natural equivalence…

We prove a new linear relation for a q-analogue of multiple zeta values. It is a q-extension of the restricted sum formula obtained by Eie, Liaw and Ong for multiple zeta values.

In this paper we define a continuous version of multiple zeta functions. They can be analytically continued to meromorphic functions on $\mathbb{C}^r$ with only simple poles at some special hyperplanes. The evaluations of these functions at…

We construct a functor that associates to any dg cooperad of dg commutative algebras (satisfying some conditions) an augmented commutative algebra. When applied to the cohomology operad of Francis Brown's moduli spaces it produces an…

The relationship between the Ohno relation and multiple polylogarithms are discussed. Using this relationship, the algebraic reduction of the Ohno relation is given.

Rooted tree maps assign to an element of the Connes-Kreimer Hopf algebra of rooted trees a linear map on the noncommutative polynomial algebra in two letters. Evaluated at any admissible word these maps induce linear relations between…

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.

In this paper, we give identities involving cyclic sums of regularized multiple zeta values of depth less than $5$. As a corollary, we present two kinds of extensions of Hoffman's theorem for symmetric sums of multiple zeta values for this…

We prove that the category of mixed Tate motives over $\Z$ is spanned by the motivic fundamental group of $\Pro^1$ minus three points. We prove a conjecture by M. Hoffman which states that every multiple zeta value is a $\Q$-linear…

According to Hoffman's (2,3)-conjecture, the so-called double shuffle relations should imply that every multiple zeta value should express effectively in terms of multizetas whose entries are equal to either 2 or 3, with some explicitly…

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…

In this paper, we will study finite multiple $T$-values (MTVs) and their alternating versions, which are level two and level four variations of finite multiple zeta values, respectively. We will first provide some structural results for…

In this paper, we establish some expressions of series involving harmonic numbers and Stirling numbers of the first kind in terms of multiple zeta values, and present some new relationships between multiple zeta values and multiple zeta…

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…

This article introduces an algebra of functions in one variable $c$ defined by iterated integrals of two specific differential forms depending on $c$, where the product is the shuffle product. This algebra can be seen as a common…

In this paper, we give elementary proofs of Zagier's formula for multiple zeta values involving Hoffman element and its odd variant due to Murakami. Zagier's formula was a key ingredient in the proof of Hoffman's conjecture. Moreover, using…

In this paper, we prove that certain parametrized multiple series which generalize multiple zeta values satisfy the same relation as Ohno's relation for multiple zeta values. This is a parametrized generalization of Ohno's relation for…