A central limit theorem for the Birkhoff sum of the Riemann zeta-function over a Boolean type transformation

Abstract: We prove a central limit theorem for the real and imaginary part and the absolute value of the Riemann zeta-function ξ sampled along a vertical line in the critical strip with respect to an ergodic transformation similar to the Boolean transformation, i.e. we have an ergodic transformation T: R->R and consider ξ(c+i T^n(x)) for different n and fixed c and x. Our results complement results by Steuding who has first studied this system and has proven a strong law of large numbers. As a side result we state a general central limit theorem for a class of unbounded observables on the real line over the same ergodic transformation. With that it is possible that the results can be generalized to other L-function.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October