Related papers: Proving dualities for qMZVs with connected sums
Following Bachmann's recent work on bi-brackets and multiple Eisenstein series, Zudilin introduced the notion of multiple q-zeta brackets, which provides a q-analog of multiple zeta values possessing both shuffle as well as quasi-shuffle…
We exhibit the double q-shuffle structure for the qMZVs recently introduced by Y. Ohno, J. Okuda and W. Zudilin.
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…
The duality relation of one-variable multiple polylogarithms was proved by Hirose, Iwaki, Sato and Tasaka by means of iterated integrals. In this paper, we give a new proof using the method of connected sums, which was recently invented by…
The multiple zeta values (MZVs) have been studied extensively in recent years. Currently there exist a few different types of $q$-analogs of the MZVs ($q$-MZVs) defined and studied by mathematicians and physicists. In this paper, we give a…
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…
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 prove some relations for the $q$-multiple zeta values ($q$MZV). They are $q$-analogues of the cyclic sum formula, the Ohno relation and the Ohno-Zagier relation for the multiple zeta values (MZV). We discuss the problem to determine the…
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…
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 establish Ohno-type identities for multiple harmonic ($q$-)sums which generalize Hoffman's identity and Bradley's identity. Our result leads to a new proof of the Ohno-type relation for $\mathcal{A}$-finite multiple zeta values recently…
Recently, Bradley studied partial sums of multiple q-zeta values and proved a duality result. In this paper, we present a generalization of his result.
We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two…
We study the algebra of certain $q$-series, called bi-brackets, whose coefficients are given by weighted sums over partitions. These series incorporate the theory of modular forms for the full modular group as well as the theory of multiple…
We know at least two ways to generalize multiple zeta(-star) values, or MZ(S)Vs for short, which are $q$-analogue and $t$-interpolation. The $q$-analogue of MZ(S)Vs, or $q$MZ(S)Vs for short, was introduced by Bradley, Okuda and Takeyama,…
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…
Recently, the author and Yamamoto invented a new proof of the duality for multiple zeta values. The technique is applicable in other series identities. In this article, we exhibit such proofs for some series identities.
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…
In the study on multiple zeta values, the duality formula is one of the families of basic relations and plays an important role in the investigation of algebraic structure of the space spanned by all multiple zeta values along with the…
One of the important research subjects in the study of multiple zeta functions is to clarify the linear relations and functional equations among them. The Schur multiple zeta functions are a generalization of the multiple zeta functions of…