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Value-distribution of Euler--Zagier type multiple zeta-functions with identical arguments on the critical line

  • Kenta Endo
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Abstract

We consider the value-distribution of the Euler--Zagier type multiple zeta-functions with identical arguments on the critical line. Mishou showed that the set of the values of the Euler--Zagier double sum with identical arguments on the critical line is dense in the complex plane under the Riemann Hypothesis. In this paper, we generalize Mishou's result to the r-fold Euler--Zagier multiple zeta-functions with identical arguments for $r geq 4$.

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Cite

BibTeXRIS
BibTeX
@misc{endo2026valuedistribution,
  title = {{Value-distribution of Euler--Zagier type multiple zeta-functions with identical arguments on the critical line}},
  author = {Kenta Endo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32242},
  eprint = {2610.32242},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32242},
}
RIS
TY  - UNPB
TI  - Value-distribution of Euler--Zagier type multiple zeta-functions with identical arguments on the critical line
AU  - Kenta Endo
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32242
UR  - https://arxiv.org/abs/2610.32242
AB  - We consider the value-distribution of the Euler--Zagier type multiple zeta-functions with identical arguments on the critical line. Mishou showed that the set of the values of the Euler--Zagier double sum with identical arguments on the critical line is dense in the complex plane under the Riemann Hypothesis. In this paper, we generalize Mishou's result to the r-fold Euler--Zagier multiple zeta-functions with identical arguments for $r geq 4$.
ER  -