Limit Theorems for L-functions in Analytic Number Theory

<p>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.</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

The Graduate School and University Center of The City University of New York

Year dc:date.available

2024

Author dc:creator

• Roberts, Asher

Advisor dc:contributor.advisor

• Louis-Pierre Arguin

Committee members dc:contributor.committeemember

• Alexander Gamburd
• Matthew Junge

• Number Theory
• Other Mathematics
• Probability
• riemann zeta function
• central limit theorem

Repository record dc:identifier

https://academicworks.cuny.edu/gc_etds/5913

OAI identifier oai:identifier

oai:academicworks.cuny.edu:gc_etds-7014