Related papers: On a reciprocity law for finite multiple zeta valu…
We prove a reciprocity relation for the twisted second moment of the Riemann Zeta function. This provides an analogue to a formula of Conrey for Dirichlet L-functions
We discuss the shuffle product of the Schur multiple zeta values, which are the special values of Schur multiple zeta functions. We first define $2$-labeled Schur posets to generalize Yamamoto's integral expression of the multiple zeta…
We study relations between the multizeta values for function fields introduced by D. Thakur. The product \zeta(a)\zeta(b) is a linear combination of multizeta values. For q=2, a full conjectural description of how the product of two zeta…
In this paper, we define a finite sum analogue of multiple polylogarithms inspired by the work of Kaneko and Zaiger and prove that they satisfy a certain analogue of the shuffle relation. Our result is obtained by using a certain partial…
The Ohno relation is a well-known relation among multiple zeta values. Hirose, Onozuka, Sato, and the author investigated the sum related to the Ohno relation and presented two types of new relations and five conjectural formulas. This…
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'…
We study relations between multizeta values for function fields introduced by D. Thakur. The F_p-span of Thakur's multizeta values is an algebra (Thakur. Shuffle relations for function field multizeta values). In particular, the product…
We discuss reflections identities of harmonic sums up to weight three. The need for this kind of identities emerges in analysis of the general structure of eigenvalue of the BFKL equation. The reflection identities decompose a product of…
The Newton series which interpolate finite multiple harmonic sums are useful in the study of multiple zeta values (MZV's). In this paper, we prove that these Newton series can be written as multiple series. As an application, we give a…
The harmonic numbers and higher-order harmonic numbers appear frequently in several areas which are related to combinatorial identities, many expressions involving special functions in analytic number theory, and analysis of algorithms. The…
It was conjectured by Bennett, Chari, and Manning that a BGG-type reciprocity holds for the category of graded representations with finite-dimensional graded components for the current algebra associated to a simple Lie algebra. We…
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 prove shuffle relations which relate a product of regularised integrals of classical symbols to regularised nested (Chen) iterated integrals, which hold if all the symbols involved have non-vanishing residue. This is true in particular…
Recently, Bradley studied partial sums of multiple q-zeta values and proved a duality result. In this paper, we present a generalization of his result.
The duality relation is a basic family of linear relations for multiple zeta values. The extended double shuffle relation (EDSR) is one of the families of relations expected to generate all linear relations among multiple zeta values, but…
Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain…
For a convex polytope P with rational vertices, we count the number of integer points in integral dilates of P and its interior. The Ehrhart-Macdonald reciprocity law gives an intimate relation between these two counting functions. A…
Riemann zeta values are generalized to multiple zeta values (MZVs) by use of nested sums, and MZVs are generalized to regularized multiple zeta values (RMZVs) by regularization of divergent infinite series. In the present paper, we prove…
We give three identities involving multiple zeta values of height one and of maximal height; an explicit formula for the height-one multiple zeta values, a regularized sum formula, and a sum formula for the multiple zeta values of maximal…
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.