Related papers: Generalisations of multiple zeta values to rooted …
In this paper we consider a family of multiple Hurwitz zeta values with bi-indices parameterized by $\mu$ with $\Ree(\mu)>0$. These values are equipped with both the $\mu$-stuffle product from their series definition and the shuffle product…
Riemann zeta values are generalized to multiple zeta values (MZVs) by use of nested sums, and MZVs are generalized to regularized multiple zeta values (RMZVs) by regularization of divergent infinite series. In the present paper, we prove…
We construct and study new generalisations to rooted trees and forests of some properties of shuffles of words. First, we build a coproduct on rooted trees which, together with their shuffle, endow them with bialgebra structure. We then…
We study two families of zeta-like multiple series -- the multiple $\rho$-values and the multiple $\eta$-values -- defined by nested sums with shifted denominators. An explicit factorial formula for $\rho$ reveals its intrinsic…
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…
In this paper, we investigate the sums of mutliple zeta(-star) values of height one: $Z_{\pm}(n)=\sum_{a+b=n} (\pm 1)^b\zeta(\{1\}^a,b+2)$, $Z_{\pm}^{\star}(n)=\sum_{a+b=n} (\pm 1)^b\zeta^{\star}(\{1\}^a,b+2)$. In particular, we prove that…
We introduce an algebraic formulation of cyclic sum formulas for multiple zeta values and for multiple zeta-star values. We also present an algebraic proof of cyclic sum formulas for multiple zeta values and for multiple zeta-star values by…
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…
One of the most interesting formulas for multiple zeta values is the sum formula proved by Granville and Zagier independently in 1990s. Many variations and generalizations of it have been found since then. In this paper, we will provide a…
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…
We consider a cyclic analogue of multiple zeta values (CMZVs), which has two kinds of expressions; series and integral expression. We prove an `integral$=$series' type identity for CMZVs. By using this identity, we construct two classes of…
We derive two formulas for the weighted sums of rooted spanning forests of particular sequence of graphs by using the matrix tree theorem. We consider cycle graphs with edges so called the pendant edges. One of our formula can be described…
We evaluate the multiple zeta values $\zeta(\{2\}^k)$ by proving a certain factorization property. The proof uses a combinatorial bijection and elementary telescoping series. We show how the infinite product for the sine function in fact…
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 $\zeta(2,...,2,3,2,...,2)$.
The shuffle algebra on positive integers encodes the usual multiple zeta values (MZVs) (with positive arguments) thanks to the representations of MZVs by iterated Chen integrals of Kontsevich. Together with the quasi-shuffle (stuffle)…
Multiple zeta values (MZVs for short) can be represented as iterated integrals of $\mathbb{Q}$-rational algebraic differential forms on $\mathbb{P}^1(\mathbb{C})\setminus\{0, 1, \infty\}$. This interpretation allows us to consider MZVs…
Multiple zeta values have been studied by a wide variety of methods. In this article we summarize some of the results about them that can be obtained by an algebraic approach. This involves "coding" the multiple zeta values by monomials in…
In this paper, we study the multiple $L$-values and the multiple zeta values of level $N$. We set up the algebraic framework for the double shuffle relations of the multiple zeta values of level $N$. Using the regularized double shuffle…
We prove and generalize several recent conjectures of Z.-W. Sun surrounding binomial coefficients and harmonic numbers. We show that Sun's series and their analogs can be represented as cyclotomic multiple zeta values of levels…
In this paper we use the generating functions and the double shuffle relations satisfied the multiple zeta values to derive some new families of identities.