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

Keita Nakai

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arXiv · 2607.20041

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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Keita Nakai. 2026-07-22. On the value distribution of the Riemann zeta-function with general shifts. https://arxiv.org/abs/2607.20041

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