Duality theorems of multiple zeta values with parameters

TL;DR

This paper extends the theory of multiple zeta values by introducing parameters and additional factors, proving generalized duality theorems and relations, and evaluating special sums in terms of Riemann zeta values.

Contribution

It presents new generalizations of duality theorems for multiple zeta values using parameters and additional factors, expanding the theoretical framework.

Findings

Generalized duality theorems for multiple zeta values

Relations among multiple zeta values involving parameters

Evaluation of special sums in terms of Riemann zeta values

Abstract

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 to evaluate some special (truncated) sums in terms of Riemann zeta values of different weights.