Primes in arithmetic progressions to smooth moduli
Speaker: Julia Stadlmann
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
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.
