On the mean values of the Barnes multiple zeta function

TL;DR

This paper investigates the asymptotic behavior of the mean square values of Barnes multiple zeta functions, highlighting their connection to the Riemann zeta function.

Contribution

It establishes the asymptotic behavior of mean square values of Barnes multiple zeta functions, advancing understanding of their properties.

Findings

Derived asymptotic formulas for mean square values

Connected Barnes multiple zeta functions to the Riemann zeta function

Enhanced understanding of the functions' asymptotic behavior

Abstract

The asymptotic behavior of the mean values of multiple zeta functions is of significant interest due to its close connection with the Riemann zeta function. In this paper, we establish asymptotic behavior of the mean square values of Barnes multiple zeta functions.