# Primes in arithmetic progressions to smooth moduli

Date: Mon, Mar 4, 2024

Location: PIMS, University of Lethbridge, Zoom, Online

Conference: Analytic Aspects of L-functions and Applications to Number Theory

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory

### Abstract:

The twin prime conjecture asserts that there are infinitely many primes p for which p+2 is also prime. This conjecture appears far out of reach of current mathematical techniques. However, in 2013 Zhang achieved a breakthrough, showing that there exists some positive integer h for which p and p+h are both prime infinitely often. Equidistribution estimates for primes in arithmetic progressions to smooth moduli were a key ingredient of his work. In this talk, I will sketch what role these estimates play in proofs of bounded gaps between primes. I will also show how a refinement of the q-van der Corput method can be used to improve on equidistribution estimates of the Polymath project for primes in APs to smooth moduli.