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On the distribution of the zeros of the Euler double zeta-function ζ2(s,s)
Abstract
We investigate the distribution of zeros of the function ζ2(s,s), namely the function defined by putting s1=s2=s in the Euler double zeta-function ζ2(s1,s2). Our theorems provide refinements of observations, obtained numerically in a previous paper by the first author and M. Shōji, with rigorous theoretical proofs.
Related
- Lower-order terms in mean-square formulas for the Euler--Zagier double zeta-function and regularized multiple zeta values
- More than 8/9 zeros of the Riemann zeta function are simple or on the critical line
- One-level density of zeros of the Riemann zeta function weighted by its special values
- Half-sized gaps between zeros of the Riemann zeta function
- Simple critical zeros and distinct zeros of the Riemann zeta function in short intervals
BibTeX
@misc{matsumoto2026distribution,
title = {{On the distribution of the zeros of the Euler double zeta-function $ζ_2(s,s)$}},
author = {Kohji Matsumoto and Tomokazu Onozuka and Isao Wakabayashi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33324},
eprint = {2609.33324},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33324},
}
RIS
TY - UNPB
TI - On the distribution of the zeros of the Euler double zeta-function ζ_2(s,s)
AU - Kohji Matsumoto
AU - Tomokazu Onozuka
AU - Isao Wakabayashi
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33324
UR - https://arxiv.org/abs/2609.33324
AB - We investigate the distribution of zeros of the function ζ_2(s,s), namely the function defined by putting s_1=s_2=s in the Euler double zeta-function ζ_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.
ER -