Primes in arithmetic progressions to smooth moduli

Date/heure
23 novembre 2023
14:30 - 15:30

Lieu
Salle Döblin

Oratrice ou orateur
Julia Stadlmann (Université d'Oxford)

Catégorie d'évènement
Séminaire de Théorie des Nombres de Nancy-Metz


Résumé

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.