Florent Jouve: Moments in the Chebotarev density Theorem

Abstract:

 I will report on joint work with Régis de La Bretèche and Daniel Fiorilli in which we consider weighted moments for the distribution of Frobenius elements in conjugacy classes of Galois groups of normal number field extensions. The question is inspired by results of Hooley and recent progress due to de La Bretèche–Fiorilli concerning moments for the distribution of primes in arithmetic progressions. As in the latter case, our results are conditional on GRH and confirm that the moments considered should be Gaussian. Time permitting we will mention another notion of moments for which particular Galois group structures exclude a Gaussian behaviour.