Dissertations, Theses, and Capstone Projects
Date of Degree
9-2024
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
Louis-Pierre Arguin
Committee Members
Alexander Gamburd
Matthew Junge
Subject Categories
Number Theory | Other Mathematics | Probability
Keywords
probability, number theory, riemann zeta function, central limit theorem
Abstract
We use the method of Radziwill and Soundararajan to prove Selberg’s central limit theorem for the real part of the logarithm of the Riemann zeta function on the critical line in the multivariate case. This gives an alternate proof of a result of Bourgade. An upshot of the method is to determine a rate of convergence in the sense of the Dudley distance. This is the same rate Selberg claims using the Kolmogorov distance. We also achieve the same rate of convergence in the case of Dirichlet L-functions. Assuming the Riemann hypothesis, we improve the rate of convergence by using an approximation for the logarithm of zeta given by Selberg.
Recommended Citation
Roberts, Asher, "Limit Theorems for L-functions in Analytic Number Theory" (2024). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/5913