On the distribution of the zeros of the Euler double zeta-function ${\zeta }_2(s,s)$

Abstract

We investigate the distribution of zeros of the function ${\zeta }_2(s,s)$, namely the function defined by putting $s_1=s_2=s$ in the Euler double zeta-function ${\zeta }_2(s_1,s_2)$. Our theorems provide refinements of observations, obtained numerically in a previous paper by the first author and M. Shōji, with rigorous theoretical proofs.