Numerical computations on the zeros of the Euler double zeta-function II

TL;DR

This paper investigates the zeros of the double zeta-function in two variables, extending previous work by numerically analyzing zero-divisors and their approach to specific points related to the Riemann zeta-function.

Contribution

It provides the first detailed numerical analysis of zero-divisors of the double zeta-function in the general two-variable case, revealing their asymptotic behavior.

Findings

Zero-divisors approach points with s_2=0

Some approach solutions of ζ(s_2)=1

Numerical evidence extends understanding of double zeta zeros

Abstract

We study the behavior of zero-divisors of the double zeta-function $\zeta_2(s_1,s_2)$. In our former paper \cite{MatSho14} we studied the case $s_1=s_2$, but in the present paper we consider the more general two variable situation. We carry out numerical computations in order to trace the behavior of zero-divisors. We observe that some divisors approach the points with $s_2=0$, while other divisors approach the points which are solutions of $\zeta(s_2)=1$.