Related papers: Multiple $T$-values and iterated log-tangent integ…
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…
In this work we discuss a parameter $\sigma$ on weighted $k$-element multisets of $[n]= \{1,\dots ,n\}$. The sums of weighted $k$-multisets are related to $k$-subsets, $k$-multisets, as well as special instances of truncated interpolated…
We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some…
This note is a compilation of related research on modular relations for multiple zeta values. Roughly speaking, modular relations are (homogeneous) linear relations of multiple zeta values of fixed weight whose coefficients are `originated'…
In this paper, we formally introduce the notion of Ap{\'e}ry-like sums and we show that every multiple zeta values can be expressed as a $\bf Z$-linear combination of them. We even describe a canonical way to do so. This allows us to put in…
The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case,…
We study logarithmic integrals of the form $\int_0^1 x^i\ln^n(x)\ln^m(1-x)dx$. They are expressed as a rational linear combination of certain rational numbers $(n,m)_i$, which we call tiered binomial coefficients, and products of the zeta…
Hirose, Murahara, and Saito proved that some $t$-adic symmetric multiple zeta values, for indices in which $1$ and $3$ appear alternately in succession, can be expressed as polynomials in Riemann zeta values, and conjectured similar…
Multiple zeta-star values are variants of multiple zeta values which allow equality in the definition. Similar to the theory of continued fractions, every real number which is greater than $1$ can be realized as an unique infinite multiple…
Interpolated multiple $q$-zeta values are deformation of multiple $q$-zeta values with one parameter, $t$, and restore classical multiple zeta values as $t = 0$ and $q \to 1$. In this paper, we discuss generating functions for sum of…
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…
This paper introduces the notion of tubular eigenvalues of third-order tensors with respect to T-products of tensors and analyzes their properties. A focus of the paper is to discuss relations between tubular eigenvalues and two alternative…
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…
Recently, Maesaka, Seki and Watanabe discovered a surprising equality between multiple harmonic sums and certain Riemann sums which approximate the iterated integral expression of the multiple zeta values. In this paper, we describe the…
The special values of multiple polylogarithms, which including multiple zeta values, appear some fields of mathematics and physics. Many kinds of their linear relations are investigated as well as their algebraic relations. From the…
Multiple zeta values arise as special values of polylogarithms defined on Riemann surfaces of various genera. Building on the vast knowledge for classical and elliptic multiple zeta values, we explore a canonical extension of the formalism…
Multiple zeta values have been studied by a wide variety of methods. In this article we summarize some of the results about them that can be obtained by an algebraic approach. This involves "coding" the multiple zeta values by monomials in…
Multiple q-zeta values are a 1-parameter generalization (in fact, a q-analog) of the multiple harmonic sums commonly referred to as multiple zeta values. These latter are obtained from the multiple q-zeta values in the limit as q tends to…
We introduce adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values. They are two variants of cyclotomic multiple zeta values, closely related to each other. They arise as key tools for the study of $p$-adic…
We define the interpolated polynomial multiple zeta values as a generalization of all of multiple zeta values, multiple zeta-star values, interpolated multiple zeta values, symmetric multiple zeta values, and polynomial multiple zeta…