Gower uniformity of primes in short intervals and in arithmetic progressions
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 either short intervals or arithmetic progressions. These can be viewed as generalizations of classical problems, such as counting primes in short intervals, and the Bombieri-Vinogradov theorem. This is based on joint works with Kaisa Matomaki and with Joni Teravainen.
邵煊程，University of Kentucky
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