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

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.