On the parity result for multiple Dirichlet series

TL;DR

This paper explores the parity properties of multiple Dirichlet series, including special cases like multiple zeta functions and root system zeta values, providing explicit expressions in terms of simpler series.

Contribution

It presents new results on the parity phenomenon for multiple Dirichlet series and offers explicit formulas relating complex series to lower series.

Findings

Established parity results for various multiple Dirichlet series.

Derived explicit expressions linking complex series to simpler ones.

Unified different types of multiple zeta and root system zeta values.

Abstract

In this paper, we discuss the parity result for multiple Dirichlet series which contains some special values of multiple zeta functions as special cases, Mordell--Tornheim type of multiple zeta values, zeta values of the root systems and so on. Moreover, we can give explicit expression in terms of lower series by using main theorem.