A central limit theorem for the Birkhoff sum of the Riemann zeta-function over a Boolean type transformation. Issue 4 (1st October 2020)

• Record Type: Journal Article
• Authors: Schindler, Tanja I.
• Is Part Of: Dynamical systems. Volume 35:Issue 4(2020)
• Page Start: 682
• Page End: 703
• Publication Date: 2020-10-01
• Subjects: central limit theorem -- Riemann zeta-function -- transfer operator -- Boolean transformation; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2020.1780198
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: We prove a central limit theorem for the real and imaginary part and the absolute value of the Riemann zeta-function sampled along a vertical line in the critical strip with respect to an ergodic transformation similar to the Boolean transformation. This result complements a result by Steuding who has proven a strong law of large numbers for the same system. 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. The proof is based on an isomorphism between the Boolean type transformation and the doubling map and on the transfer operator method.