Related papers: A note on evaluations of multiple zeta values

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…

In this paper we shall define the renormalization of the multiple $q$-zeta values (M$q$ZV) which are special values of multiple $q$-zeta functions $\zeta_q(s_1,...,s_d)$ when the arguments are all positive integers or all non-positive…

In recent years, a variety of variants of multiple zeta values (MZVs) have been defined and studied. One way to produce these variants is to restrict the indices in the definition of MZVs to some fixed parity pattern, which include…

By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta…

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…

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,…

The cyclic insertion conjecture of Borwein, Bradley, Broadhurst and Lison\v{e}k states that inserting all cyclic shifts of some fixed blocks of 2's into the multiple zeta value {\zeta}(1,3,...,1,3) gives an explicit rational multiple of a…

Riemann zeta values are generalized to multiple zeta values (MZVs) by use of nested sums, and MZVs are generalized to regularized multiple zeta values (RMZVs) by regularization of divergent infinite series. In the present paper, we prove…

We prove that every multiple zeta value is a $\mathbb{Z}$-linear combination of $\zeta(k_1,\dots, k_r)$ where $k_i\geq 2$. Our proof also yields an explicit algorithm for such an expansion. The key ingredient is to introduce modified…

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…

In this paper, we study the evaluation formulas of the interpolated multiple zeta values and the interpolated multiple $t$-values with indices involving $1,2,3$. To get these evaluations, we derive the corresponding algebraic relations in…

In this paper we define a continuous version of multiple zeta functions. They can be analytically continued to meromorphic functions on $\mathbb{C}^r$ with only simple poles at some special hyperplanes. The evaluations of these functions at…

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…

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 evaluate several classes of high weight hypergeometric series via Multiple Zeta Values.

In this paper we prove some new identities for multiple zeta values and multiple zeta star values of arbitrary depth by using the methods of integral computations of logarithm function and iterated integral representations of series. By…

Bowman and Bradley obtained a remarkable formula among multiple zeta values. The formula states that the sum of multiple zeta values for indices which consist of the shuffle of two kinds of the strings $\{1,3,\ldots,1,3\}$ and…

We evaluate the multiple zeta values $\zeta(\{2\}^k)$ by proving a certain factorization property. The proof uses a combinatorial bijection and elementary telescoping series. We show how the infinite product for the sine function in fact…

We prove a new class of relations among multiple zeta values (MZV's) which contains Ohno's relation. We also give the formula for the maximal number of independent MZV's of fixed weight, under our new relations. To derive our formula for…

In this paper, we give the values of a certain kind of $q$-multiple zeta functions at roots of unity. Various multiple zeta values have been proposed and studied by many researchers, but these multiple zeta values naturally arise from…