Related papers: Finite and symmetric Mordell-Tornheim multiple zet…
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…
We prove that the $\mathbb{Q}$-vector space generated by the multiple zeta values is generated by the finite real multiple zeta values introduced by Kaneko and Zagier.
In this paper, we establish some new identities of integrals involving multiple polylogarithm functions and their level two analogues in terms of Hurwitz-type multiple zeta (star) values. Using these identities, we provide new proofs of the…
For several evaluations of special values and several relations known only in $\mathcal{A}_n$-multiple zeta values or $\mathcal{S}_n$-multiple zeta values, we prove that they are uniformly valid in $\mathcal{F}_n$-multiple zeta values for…
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…
We explore the theory of multiple zeta values (MZVs) and some of their $q$-generalisations. Multiple zeta values are numerical quantities that satisfy several combinatorial relations over the rationals. These relations include two…
Multiple $T$-values, a variant of multiple zeta values of level two, were introduced and studied by Kaneko and Tsumura. This paper will introduce iterated log-tangent integrals and discuss their relations with multiple $T$-values. We will…
We prove the Ohno-type relation for the interpolated multiple zeta values, which was introduced first by Yamamoto. Same type results for finite multiple zeta values are also given. Moreover, these relations give the sum formula for…
Multiples zeta values and alternating multiple zeta values in positive characteristic were introduced by Thakur and Harada as analogues of classical multiple zeta values of Euler and Euler sums. In this paper we determine all linear…
Explicit evaluations of the Tornheim-like double series in the form \[ \sum_{n,m=1}^\infty \frac{H_{n+m+s}}{nm\left( n+m+s \right)},\ s\in \mathbb{N\cup } \left\{ 0 \right\} \] and their extensions are given. Furthermore, series of the type…
Let $l\ge 1$ be an integer. For any multiple index $\mathbf{s}=(s_1,s_2,\cdots,s_l)\in\mathbb{Z}_{\geq 1}^l$ with $s_l>1$, the multiple zeta value (MZV for short) is defined by \begin{align*} \zeta(s_1,s_2,\cdots,s_l):=\sum_{1\leq…
We consider the symmetric multiple zeta values in $\mathcal{S}_m$ without modulo $\pi^2$ reduction for indices in which $1$ and $3$ appear alternately. We investigate those values that can be expressed as a polynomial of the Riemann zeta…
We combine the powerful method of Wilf-Zeilberger pairs with systematic theory of multiple zeta values to prove a large number of series identities due to Z.W. Sun, many of them have been long standing conjectures.
Recently, a new kind of multiple zeta value level two $T({\bf k})$ (which is called multiple $T$-values) was introduced and studied by Kaneko and Tsumura. In this paper, we define a kind of alternating version of multiple $T$-values, and…
We present a new "integral=series" type identity of multiple zeta values, and show that this is equivalent in a suitable sense to the fundamental theorem of regularization. We conjecture that this identity is enough to describe all linear…
We present several conjectures on multiple q-zeta values and on the role they play in certain problems of enumerative geometry.
We study multiple zeta values (MZVs) from the viewpoint of zeta-functions associated with the root systems which we have studied in our previous papers. In fact, the $r$-ple zeta-functions of Euler-Zagier type can be regarded as the…
In this note we introduce multi-interpolated multiple zeta values. We provide a basic decomposition of these objects involving ordered partitions. We also obtain identities for special instances of multi-interpolated multiple zeta values…
We study the asymptotic behavior of a multiple series of Mordell-Tornheim type and its integral analogue at x=0. Our approach is to show a relation between the multiple series and its integral analogue by using Abel's summation formula, and…
The multiple zeta values are generalizations of the values of the Riemann zeta function at positive integers. They are known to satisfy a number of relations, among which are the cyclic sum formula. The cyclic sum formula can be stratified…