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PreprintarXiv licencearXiv

On the value distribution of the Riemann zeta-function with general shifts

  • Keita Nakai
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Abstract

This paper studies the value distribution of the Riemann zeta-function under general shifts. We establish discrepancy estimates for the Bohr--Jessen limit theorem for a broad class of shifts. We also prove a universality theorem for logarithmic-power shifts, which are not covered by previous universality results for general shifts. Furthermore, we obtain a quantitative Bohr--Jessen limit theorem for logarithmic-power shifts.

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Cite

BibTeXRIS
BibTeX
@misc{nakai2026value,
  title = {{On the value distribution of the Riemann zeta-function with general shifts}},
  author = {Keita Nakai},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.20041},
  eprint = {2607.20041},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.20041},
}
RIS
TY  - UNPB
TI  - On the value distribution of the Riemann zeta-function with general shifts
AU  - Keita Nakai
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2607.20041
UR  - https://arxiv.org/abs/2607.20041
AB  - This paper studies the value distribution of the Riemann zeta-function under general shifts. We establish discrepancy estimates for the Bohr--Jessen limit theorem for a broad class of shifts. We also prove a universality theorem for logarithmic-power shifts, which are not covered by previous universality results for general shifts. Furthermore, we obtain a quantitative Bohr--Jessen limit theorem for logarithmic-power shifts.
ER  -