Related papers: Balanced multiple q-zeta values

Interpolated multiple zeta values can be regarded as interpolation polynomials of multiple zeta values and multiple zeta-star values. In this paper, we give some algebraic relations of interpolated multiple zeta values, such as the…

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 survey article, we discuss the algebraic structure of q-analogues of multiple zeta values, which are closely related to derivatives of Eisenstein series. Moreover, we introduce the formal double Eisenstein space, which generalizes…

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…

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…

We establish a new class of relations among the multiple zeta values \zeta(k_1,k_2,...,k_n), which we call the cyclic sum identities. These identities have an elementary proof, and imply the "sum theorem" for multiple zeta values. They also…

In this paper, we introduce the symmetric multiple Eisenstein series, a variant of the multiple Eisenstein series. As a fundamental result, we show that they satisfy the linear shuffle relation. As a case study, we investigate the vector…

Multiple Eisenstein series are holomorphic functions in the complex upper-half plane, which can be seen as a crossbreed between multiple zeta values and classical Eisenstein series. They were originally defined by Gangl-Kaneko-Zagier in…

Interpolated multiple $q$-zeta values are deformation of multiple $q$-zeta values with one parameter, $t$, and restore classical multiple zeta values as $t = 0$ and $q \to 1$. In this paper, we discuss generating functions for sum of…

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)…

Extended double shuffle relations for multiple zeta values are obtained by the fact that any product of regularized multiple zeta values has two different representations, and the case of two-fold product is considered in general. In this…

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…

We present several conjectures on multiple q-zeta values and on the role they play in certain problems of enumerative geometry.

We derive an explicit formula for the quasi--shuffle product satisfied by Schlesinger--Zudilin Multiple~$q$-Zeta Values, expressed in terms of partition data. To achieve this, we interpret Schlesinger--Zudilin Multiple~$q$-Zeta Values as…

This survey gives a self-contained introduction to q-analogues of multiple zeta values (qMZVs). For this, we consider most common models of qMZVs in a unified setup going back to Bachmann and K\"uhn, such as a related quasi-shuffle product…

Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuffle…

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…

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…

We study the double shuffle relations satisfied by the double zeta values of level 2, and introduce the double Eisenstein series of level 2 which satisfy the double shuffle relations. We connect the double Eisenstein series to modular forms…

The classical quasi-shuffle algebra for multiple zeta values have a well-known Hopf algebra structure. Recently, the shuffle algebra for multiple zeta values are also equipped with a Hopf algebra structure. This paper shows that these two…