A celebrated theorem of Green-Tao asserts that the set of primes is Gowers uniform, allowing them to count asymptotically the number of k-term arithmetic progressions in primes up to a threshold. In this talk I will discuss results of this type for primes restricted to arithmetic progressions. These can be viewed as generalizations of the classical Bombieri-Vinogradov theorem. I will also discuss a number of applications; for example, the set of primes p obeying explicit bounded gaps.
This is joint work with Joni Teravainen.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
