Related papers: Relationship between renormalized values of shuffl…

We introduce a $q$-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple $q$-zeta values satisfy a $q$-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the…

We establish some identities of Euler related sums. By using these identities, we discuss the closed form representations of sums of harmonic numbers and reciprocal parametric binomial coefficients through parametric harmonic numbers,…

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…

It is conjectured that the regularized double shuffle relations give all algebraic relations among the multiple zeta values, and hence all other algebraic relations should be deduced from the regularized double shuffle relations. In this…

In this paper, we study the evaluation formulas of the interpolated multiple zeta values and the interpolated multiple $t$-values with indices involving $1,2,3$. To get these evaluations, we derive the corresponding algebraic relations in…

We discuss the shuffle product of the Schur multiple zeta values, which are the special values of Schur multiple zeta functions. We first define $2$-labeled Schur posets to generalize Yamamoto's integral expression of the multiple zeta…

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.

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 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…

We study a general type of series and relate special cases of it to Stirling series, infinite series discussed by Choi and Hoffman, and also to special values of the Arakawa-Kaneko zeta function, complementing and generalizing earlier…

Symmetric multiple zeta values (SMZVs) are elements in the ring of all multiple zeta values modulo the ideal generated by $\zeta(2)$ introduced by Kaneko-Zagier as counterparts of finite multiple zeta values. It is known that symmetric…

We begin by shortly recalling a generalized mean value inequality for subharmonic functions, and two applications of it: first a weighted boundary behavior result (with some new references and remarks), and then a borderline case result to…

Bachmann and Tasaka discovered a relationship between multiple Eisenstein series (MES) of level 1 and formal iterated integrals corresponding to multiple zeta value. They also constructed shuffle regularized MES of level 1, which satisfies…

We study the Hurwitz-type analogue of Schur multiple zeta-functions involving shifting parameters. We extend various formulas, known for ordinary Schur multiple zeta-functions, to the case of Hurwitz type. We also mention unpublished…

We introduce a new deformation of multiple zeta value (MZV). It has one parameter $\omega$ satisfying $0<\omega<2$ and recovers MZV in the limit as $\omega \to +0$. It is defined in the same algebraic framework as a $q$-analogue of multiple…

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 give an explicit formula for the shuffle relation in a general double shuffle framework that specializes to double shuffle relations of multiple zeta values and multiple polylogarithms. As an application, we generalize the well-known…

The alternating multiple harmonic sums are partial sums of the infinite series defining the Euler sums which are the alternating version of the multiple zeta value series. In this paper, we present some systematic structural results of the…

We construct bases of quasi-symmetric functions whose product rule is given by the shuffle of binary words, as for multiple zeta values in their integral representations, and then extend the construction to the algebra of free…

In this paper we obtain a recursive formula for the shuffle product and apply it to derive two restricted decomposition formulas for multiple zeta values (MZVs). The first formula generalizes the decomposition formula of Euler and is…