Related papers: Duality and (q-)multiple zeta values

Ohno's relation is a generalization of both the sum formula and the duality formula for multiple zeta values. Oyama gave a similar relation for finite multiple zeta values, defined by Kaneko and Zagier. In this paper, we prove relations of…

Recently, Kaneko and Tsumura introduced multiple $\widetilde{T}$-values, another kind of poly-Euler numbers and the related Arakawa-Kaneko type zeta function. It is shown that each of them satisfies similar formulas to those of multiple…

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 introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones. The quasi-shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision…

We obtain a class of quadratic relations for a q-analogue of multiple zeta values (qMZV's). In the limit q->1, it turns into Kawashima's relation for multiple zeta values. As a corollary we find that qMZV's satisfy the linear relation…

The derivation relation is a well known relation among multiple zeta values, which was first obtained by Ihara, Kaneko and Zagier. The analogous formula for finite multiple zeta values, which we call the derivation relation for finite…

We introduce derivations on the algebra of multiple harmonic q-series and show that they generate linear relations among the q-series which contain the derivation relations for a q-analogue of multiple zeta values due to Bradley. As a…

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 2003, Zudilin presented a $q$-analogue of Euler's identity for one of the variants of $q$-double zeta function. This article focuses on exploring identities related to another variant of $q$-double zeta function and its star variant.…

This paper offers a Hopf algebraic interpretation of a functional equation of multiple zeta functions, motivated by the classical symmetry of the Riemann zeta function. Starting from the extended shuffle algebra that encodes multiple zeta…

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…

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 prove and conjecture several relations between multizeta values for $\mathbb{F}_q[t]$, focusing on zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or equivalently algebraic). In particular,…

We introduce the algebra of formal multiple Eisenstein series and study its derivations. This algebra is motivated by the classical multiple Eisenstein series, introduced by Gangl-Kaneko-Zagier as a hybrid of classical Eisenstein series and…

We give a new proof of the duality of multiple zeta values, which makes no use of the iterated integrals. The same method is also applicable to Ohno's relation for ($q$-)multiple zeta values.

In their seminal paper "Double zeta values and modular forms" Gangl, Kaneko and Zagier defined a double Eisenstein series and used it to study the relations between double zeta values. One of their key ideas is to study the formal double…

In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…

In 2015, Bachmann \cite{Ba3} conjectured that the~$\Q$-vector space~$\Zq$ of (formal)~$q$-analogues of Multiple Zeta Values (\qmzv s) is spanned by a very particular set compared to known spanning sets. In this work, we prove that this…

We study a class of q-analogues of multiple zeta values given by certain formal q-series with rational coefficients. After introducing a notion of weight and depth for these q-analogues of multiple zeta values we present dimension…

Formal multiple zeta values allow to study multiple zeta values by algebraic methods in a way that the open question about their transcendence is circumvented. In this note we show that Hoffman's basis conjecture for formal multiple zeta…