On an analog of the Arakawa-Kaneko zeta function and relations of some multiple zeta values

TL;DR

This paper explores analogs of the Arakawa-Kaneko zeta function, establishing new relations among multiple zeta values and extending the framework to Miyagawa-type and more general zeta functions.

Contribution

It introduces Miyagawa-type zeta functions and connects them to Ito's zeta functions, advancing the understanding of relations among multiple zeta values.

Findings

Derived Miyagawa-type zeta functions analogous to Arakawa-Kaneko functions.

Established relations among Miyagawa-type multiple zeta values.

Linked Ito's zeta functions to a broader class of zeta functions.

Abstract

T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an analog of the Arakawa-Kaneko zeta function. One is to find an analog of the Arakawa-Kaneko zeta function of Miyagawa-type (defined by T. Miyagawa) and to obtain a relation among Miyagawa-type MZVs. The other is to find a class of zeta functions to which Ito's zeta functions of the case of general index are related.