Mean value theorems for the Apostol-Vu double zeta-function and its application

TL;DR

This paper derives mean square values for Apostol-Vu and Mordell-Tornheim double zeta-functions, advancing understanding of their average behaviors and properties.

Contribution

It introduces new mean square value results for specific double zeta-functions, expanding the analytical framework for these functions.

Findings

Mean square values computed for Apostol-Vu double zeta-function

Mean square values computed for Mordell-Tornheim double zeta-function

Enhanced understanding of the average behavior of these zeta-functions

Abstract

In this paper, we obtain mean square values of the double zeta-functions of the Apostol-Vu type and the Mordell-Tornheim type.