English

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

Number Theory 2019-04-15 v3

Abstract

We study the behavior of zero-divisors of the double zeta-function ζ2(s1,s2)\zeta_2(s_1,s_2). In our former paper \cite{MatSho14} we studied the case s1=s2s_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 s2=0s_2=0, while other divisors approach the points which are solutions of ζ(s2)=1\zeta(s_2)=1.

Keywords

Cite

@article{arxiv.1606.03806,
  title  = {Numerical computations on the zeros of the Euler double zeta-function II},
  author = {Kohji Matsumoto and Mayumi Shōji},
  journal= {arXiv preprint arXiv:1606.03806},
  year   = {2019}
}

Comments

14 pages, 16 figures

R2 v1 2026-06-22T14:23:39.065Z