On a unified double zeta function of Mordell--Tornheim type

TL;DR

This paper introduces a new unified double zeta function of Mordell--Tornheim type, computes its values at non-positive integers, and explores a potential generalization of the Kaneko--Zagier conjecture across all integer points.

Contribution

It presents a novel unified double zeta function, provides explicit value computations at non-positive integers, and proposes a generalization of a significant conjecture in the field.

Findings

Computed values at non-positive integer points.

Proposed a generalization of the Kaneko--Zagier conjecture.

Introduced a new unified double zeta function of Mordell--Tornheim type.

Abstract

We introduce the unified double zeta function of Mordell--Tornheim type and compute its values at non-positive integer points. We then discuss a possible generalization of the Kaneko--Zagier conjecture for all integer points.