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

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.

26 pages