Related papers: Some relations deduced from regularized double shu…
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 this paper, we study multiple Eisenstein series, which build a natural bridge between the theory of multiple zeta values and modular forms. We prove a large family of relations among these series and propose an explicit conjectural…
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 sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.
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…
We introduce a $q$-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple $q$-zeta values satisfy a $q$-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the…
This article introduces an algebra of functions in one variable $c$ defined by iterated integrals of two specific differential forms depending on $c$, where the product is the shuffle product. This algebra can be seen as a common…
We treat desingularized multiple zeta-functions introduced by Furusho, Komori, Matsumoto and Tsumura. In this paper, we prove functional relations, which are shuffle type product formulae, between desingularized multiple zeta-functions and…
We prove a sum-shuffle formula for multiple zeta values in Tate algebras (in positive characteristic), introduced in \cite{PEL3}.This follows from an analog result for double twisted power sums, implying that an ${\mathbb{F}\_p$-vector…
This paper offers a Hopf algebraic interpretation of a functional equation of multiple zeta functions, motivated by the classical symmetry of the Riemann zeta function. Starting from the extended shuffle algebra that encodes multiple zeta…
Ohno's relation is a well-known family of relations among multiple zeta values, which can naturally be regarded as a type of duality for a certain power series which we call an Ohno sum. In this paper, we investigate $\mathbb{Q}$-linear…
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…
In this paper, we settle the problem posed by Singer which is on a comparison problem between the renormalized values of shuffle type and of harmonic type of multiple zeta functions.
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…
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…
The sum formula for multiple zeta values are derived, via the Mellin transform, from the Euler connection formula and the Landen connection formula for polylogarithms. These connection formulas for multiple polylogarithms will be considered…
The Kaneko--Zagier conjecture describes a correspondence between finite multiple zeta values and symmetric multiple zeta values. Its refined version has been established by Jarossay, Rosen and Ono--Seki--Yamamoto. In this paper, we…
Let s_1,...,s_d be d positive integers and consider the multiple Hurwitz-zeta value zeta(s_1,...,s_d;-1/2,...,-1/2)/2^w where w=s_1+...+s_d is called the weight. For d<n+1, let T(2n,d) be the sum of all these values with even arguments…
In this paper, we give a formula that connects two variants of multiple zeta values; multitangent functions and symmetric multiple zeta values. As an application of this formula, we give two results. First, we prove Bouillot's conjecture on…
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…