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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 provide a proof of a conjecture by Zhao concerning the structure of certain relations among cyclotomic multiple zeta values in weight two. We formulate this conjecture in a broader algebraic setting in which we give a natural equivalence…
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,…
In 2017, E. Panzer proved the parity theorem for multiple polylogarithms. While his proof is simple and constructive, it does not yield a general explicit formula. Inspired by M. Hirose's recent work on the parity theorem for multiple zeta…
We provide a period interpretation for multizeta values (in the function field context) in terms of explicit iterated extensions of tensor powers of Carlitz motives (mixed Carlitz-Tate t-motives). We give examples of combinatorially…
We prove an easy but interesting result about the linear independence of multiple zeta values of different weights.
Multiple modular values are a common generalisation of multiple zeta values and periods of modular forms, and are periods of a hypothetical Tannakian category of mixed modular motives. They are given by regularised iterated integrals on the…
We define a generalisation of the completed Riemann zeta function in several complex variables. It satisfies a functional equation, shuffle product identities, and has simple poles along finitely many hyperplanes, with a recursive structure…
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 paper we shall consider a few variants of the motivic multiple zeta values of level two by restricting the summation indices in the definition of multiple zeta values to some fixed parity patterns. These include Hoffman's multiple…
We give a Quillen equivalence between May and Sigurdsson's model category of parametrized spectra over BG, and Mandell, May, Schwede, and Shipley's model category of modules over the orthogonal ring spectrum \Sigma^\infty_+ G, for each…
In this paper we show that the iterated integrals on products of one variable multiple polylogarithms from 0 to 1 are actually multiple zeta values if they are convergent. In the divergent case, we define regularized iterated integrals from…
The $t$-adic symmetric multiple zeta values were defined Jarossay, which have been studied as a real analogue of $\boldsymbol{p}$-adic finite multiple zeta values. In this paper, we consider the star analogues based on several…
In this paper, we generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give…
This paper describes generalized polylogarithms, multiple polylogarithms, and multiple zeta values, along with their implementation in Maple 2018. This set of related functions is of interest in high energy physics as well as in number…
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 generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
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…
Bachmann and Tasaka discovered a relationship between multiple Eisenstein series (MES) of level 1 and formal iterated integrals corresponding to multiple zeta value. They also constructed shuffle regularized MES of level 1, which satisfies…
In this paper we use the generating functions and the double shuffle relations satisfied the multiple zeta values to derive some new families of identities.