Related papers: A Weak Euler Formula for l-adic Galois Double Zeta…
In this paper we introduce and study double tails of multiple zeta values. We show, in particular, that they satisfy certain recurrence relations and deduce from this a generalization of Euler's classical formula…
We construct an analytic approach to evaluate odd Euler sums, multiple zeta value $\zeta(3,2,\ldots,2)$ and multiple $t$-value $t\left(3,2,\ldots,2\right)$. Moreover, we also conjecture a closed expression for multiple $t$-value…
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,…
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…
In this note we shall study the Witten multiple zeta function associated to the Lie algebra so(5) defined by Matsumoto. Our main result shows that its special values at nonnegative integers are always expressible by alternating Euler sums.…
In this paper we discuss three types of the mean values of the Euler double zeta function. In order to get results we introduce three approximate formulas for this function.
We present a unified approach which gives completely elementary proofs of three weighted sum formulae for double zeta values. This approach also leads to new evaluations of sums relating to the harmonic numbers, the alternating double zeta…
We give new closed and explicit formulas for "multiple zeta values" at non-positive integers of generalized Euler-Zagier multiple zeta-functions. We first prove these formulas for a small convenient class of these multiple zeta-functions…
We prove asymptotic formulas for mean square values of the Euler double zeta-function $\zeta_2(s_0,s)$, with respect to $\Im s$. Those formulas enable us to propose a double analogue of the Lindel{\"o}f hypothesis.
We study generating functions for multiple zeta star values in general form. These generating functions provide a connection between multiple zeta star values and multiple Euler sums, which allows us to express each multiple zeta star value…
Many $\mathbb{Q}$-linear relations exist between multiple zeta values, the most interesting of which are various weighted sum formulas. In this paper, we generalized these to Euler sums and some other variants of multiple zeta values by…
In this paper we will study the double zeta values $\zeta(k,m)$ using Picard-Fuchs equation. We will give a very efficient method to evaluate $\zeta(k,1)$ (resp. $\zeta(k,2)$) in terms of the products of zeta values…
In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…
A typical formula of multiple zeta values is the sum formula which expresses a Riemann zeta value as a sum of all multiple zeta values of fixed weight and depth. Recently weighted sum formulas, which are weighted analogues of the sum…
Flajolet and Salvy pointed out that every Euler sum is a $\mathbb{Q}$-linear combination of multiple zeta values. However, in the literature, there is no formula completely revealing this relation. In this paper, using permutations and…
We study three special Dirichlet series, two of them alternating, related to the Riemann zeta function. These series are shown to have extensions to the entire complex plane and we find their values at the negative integers (or residues at…
We introduce and study "elliptic zeta values", a two-parameter deformation of the values of Riemann's zeta function at positive integers. They are essentially Taylor coefficients of the logarithm of the elliptic gamma function, and share…
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.
The double zeta function is a function of two arguments defined by a double Dirichlet series, and was first studied by Euler in response to a letter from Goldbach in 1742. By calculating many examples, Euler inferred a closed form…
The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.