Related papers: An explicit parity theorem for multiple zeta value…
We take another look at the so-called quasi-derivation relations in the theory of multiple zeta values, by giving a certain formula for the quasi-derivation operator. In doing so, we are not only able to prove the quasi-derivation relations…
We prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class…
In this paper, we provide a symmetric formula and a duality formula relating multiple zeta values and zeta-star values. Leveraging Zagier's formula for computing $\zeta^\star(\{2\}^p,3,\{2\}^q)$, we employ our theorems to establish a…
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,…
The derivation relations for multiple zeta values is proved by Ihara, Kaneko and Zagier. We prove its counterpart for finite multiple zeta values.
In this paper we define and study a Dedekind-like zeta function for the algebra of multicomplex numbers. By using the idempotent representations for such numbers, we are able to identify this zeta function with the one associated to a…
We define a class of expressions for the multiple zeta function, and show how to determine whether an expression in the class vanishes identically. The class of such identities, which we call partition identities, is shown to coincide with…
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…
Ohno's relation is a well-known relation among multiple zeta values.In this paper, we prove Ohno-type relation for finite multiple zeta values, which is conjectured by Kaneko.As a corollary, we give an alternative proof of the sum formula…
We introduce an algebraic formulation of cyclic sum formulas for multiple zeta values and for multiple zeta-star values. We also present an algebraic proof of cyclic sum formulas for multiple zeta values and for multiple zeta-star values by…
In the present paper, we prove an identity for the generating function of the quadruple zeta values. Taking homogeneous parts on both sides of the identity and substituting appropriate values for the variables, we obtain the sum formula for…
We study some classical identities for multiple zeta values and show that they still hold for zeta functions built on the zeros of an arbitrary function. We introduce the complementary zeta function of a system, which naturally occurs when…
We prove a new linear relation for multiple zeta values. This is a natural generalization of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values.
Multiple zeta values (MZVs) are real numbers which are defined by certain multiple series. Recently, many people have researched for relations among them and many relations are well known. In this paper, we get a new relation among them…
We write down the functional equation of the zeta function of a global field. This equation is implicit in Weil's ``Basic Number Theory''.
We study rather general multiple zeta-functions whose denominators are given by polynomials. The main aim is to prove explicit formulas for the values of those multiple zeta-functions at non-positive integer points. We first treat the case…
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then,…
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…
We obtain recursive formulas for the stuffle product of multiple zeta values and of multiple zeta-star values. Then we apply the formulas to prove several stuffle product formulas with one or two strings of $z_p$'s. We also describe how to…
We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two…