Department of

September 2020 October 2020 November 2020 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 5 1 2 3 1 2 3 4 5 6 7 6 7 8 9 10 11 12 4 5 6 7 8 9 10 8 9 10 11 12 13 14 13 14 15 16 17 18 19 11 12 13 14 15 16 17 15 16 17 18 19 20 21 20 21 22 23 24 25 26 18 19 20 21 22 23 24 22 23 24 25 26 27 28 27 28 29 30 25 26 27 28 29 30 31 29 30

Tuesday, October 6, 2020

**Abstract:** Since the work of Barban, Davenport and Halberstam, the variance of primes in arithmetic progressions has been widely studied and continues to be an active topic of research. However, much less is known about higher moments. Hooley established a bound on the third moment, which was later sharpened by Vaughan for a variant involving a major arcs approximation. Little is known for moments of order four or higher, other than a conjecture of Hooley. In this talk I will discuss recent joint work with Régis de la Bretèche on weighted moments of moments of primes in progressions. In particular we will show how to deduce sharp unconditional omega results on all weighted even moments in certain ranges.