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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.20041

Author: Nakai, Keita

Institution: Nagoya University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: ゼータ関数の値分布論とその応用

OpenAlex ID: W7170159207

Cites: 2

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Related to: 10