On Witten multiple zeta-functions associated with semisimple Lie algebras V

TL;DR

This paper investigates the values of Witten multiple zeta-functions associated with the G_2 root system at positive integers, extending previous work to include cases where some integers are odd, and discusses the underlying reasons for this extension.

Contribution

It provides new theorems for the values of the zeta-function at positive integers, including cases with odd integers, expanding the understanding beyond previous even-integer cases.

Findings

Extended the analysis of Witten zeta-functions to include odd integers.

Proved several new theorems for the zeta-function values at positive integers.

Discussed the underlying reasons enabling treatment of odd integer cases.

Abstract

We study the values of the zeta-function of the root system of type $G_2$ at positive integer points. In our previous work we considered the case when all integers are even, but in the present paper we prove several theorems which include the situation when some of the integers are odd. The underlying reason why we may treat such cases including odd integers is also discussed.