Related papers: Bowman-Bradley type theorem for finite multiple ze…
An explicit formula for the height-one multiple zeta values was proved by Kaneko and the second author. We give an alternative proof of this result and its generalization. We also prove its counterpart for the finite multiple zeta values.
We define finite multiple zeta values (FMZVs) associated with some combinatorial objects, which we call 2-colored rooted trees, and prove that FMZVs associated with 2-colored rooted trees satisfying certain mild assumptions can be written…
We explicitly construct a universal A-infinity deformation of Batalin-Vilkovisky algebras, with all coefficients expressed as rational sums of multiple zeta values. If the Batalin-Vilkovisky algebra that we start with is cyclic, then so is…
We compute the $k$th power-sums (for all $k>0$) over an arbitrary finite unital ring $R$. This unifies and extends the work of Brawley, Carlitz, and Levine for matrix rings [Duke Math. J. 1974], with folklore results for finite fields and…
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…
Let $r\ge 1$ be an integer. For any multiple index $\mathbf{s}=(s_1,s_2,\cdots,s_r) \in\mathbb{Z}_{\geq 1}^r$ with $s_r>1$, the multiple zeta value (MZV for short) is defined by \begin{align*} \zeta(s_1,s_2,\cdots,s_r):=\sum_{1\leq…
Let $R^{\frac{1}{2}}$ be a large integer, and $\omega$ be a nonnegative weight in the $R$-ball $B_R=[0,R]^2$ such that $\omega(B_R)\le R$. For any complex sequence $\{a_n\}$, define the quadratic exponential sum \[…
In this sequel to our recent note it is shown, in a unified manner, by making use of some basic properties of certain special functions, such as the Hurwitz zeta function, Lerch zeta function and Legendre chi function, that the values of…
We establish a short exact sequence about depth-graded motivic double zeta values of even weight relative to $\mu_2$. We find a basis for the depth-graded motivic double zeta values relative to $\mu_2$ of even weight and a basis for the…
In this paper, we investigate the sums of mutliple zeta(-star) values of height one: $Z_{\pm}(n)=\sum_{a+b=n} (\pm 1)^b\zeta(\{1\}^a,b+2)$, $Z_{\pm}^{\star}(n)=\sum_{a+b=n} (\pm 1)^b\zeta^{\star}(\{1\}^a,b+2)$. In particular, we prove that…
In this paper we prove a weighted sum formula for multiple harmonic sums modulo primes, thereby proving a weighted sum formula for finite multiple zeta values. Our proof utilizes difference equations for the generating series of multiple…
We prove an easy but interesting result about the linear independence of multiple zeta values of different weights.
In 1998, Borwein, Bradley, Broadhurst and Lison\v{e}k posed two families of conjectural identities among multiple zeta values, later generalized by Charlton using his alternating block notation. In this paper, we prove a new class of…
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…
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…
There has been an avalanche of recent research on multiple zeta values. We propose dividing identities for multiple zeta values into structural and specific types. Structural identities are valid for any generalized multiple zeta function,…
Beginning with the conjecture of Artin and Tate in 1966, there has been a series of successively more general conjectures expressing the special values of the zeta function of an algebraic variety over a finite field in terms of other…
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…
The sum formula is a well known relation in the field of the multiple zeta values. In this paper, we present its generalization for the Euler-Zagier multiple zeta function.
Xu, Yan and Zhao showed that in even weight, the multiple $T$ value $T(2, 1, \ldots, 1, \overline{1})$ is a polynomial in $\log(2)$, $\pi$, Riemann zeta values, and Dirichlet beta values. Based on low-weight examples, they conjectured that…