## L-functions in Analytic Number Theory: Asif Zaman

- Date: 02/15/2023
- Time: 12:00

University of Lethbridge

A uniform prime number theorem for arithmetic progressions

I will describe a version of the prime number theorem for arithmetic progressions that is uniform enough to deduce the Siegel-Walfisz theorem, Hoheisel's asymptotic for short intervals, a Brun-Titchmarsh bound and Linnik's bound for the least prime in an arithmetic progression. The proof combines Vinogradov-Korobov's zero-free region, a log-free zero density estimate and the Deuring-Heilbronn zero repulsion phenomenon. This is joint work with Jesse Thorner.

This event is part of the PIMS CRG Group on L-Functions in Analytic Number Theory. More details can be found on the webpage here: https://sites.google.com/view/crgl-functions/crg-weekly-seminar?authuser...