Primes in arithmetic progressions and bounded gaps
Appears in collection : Prime numbers and arithmetic randomness / Nombres premiers et aléa arithmétique
Following Zhang's breakthrough on bounded gaps between primes, much work has gone into improving upper bounds on the smallest integer which appears infinitely often as the gap between a given number of primes. Equidistribution estimates for primes in certain arithmetic progressions are a key ingredient of Zhang's proof and later work of Polymath. In this talk, I will highlight how bounded gaps and primes in arithmetic progressions are linked, and I will discuss obstacles and recent successes in using various types of old and new equistribution estimates to improve on the results of Polymath for bounded gaps between primes.
