Philadelphia Area Number Theory Seminar

Wednesday, December 5, 2018 - 2:15pm

Alexandra Florea

Columbia University

I will talk about some recent work with Chantal David and Matilde Lalin about the mean value of L-functions associated to cubic characters over Fq[t] when q ≡ 1 (mod 3). I will explain how to obtain an asymptotic formula which relies on obtaining cancellation in averages of cubic Gauss sums over functions fields. I will also talk about the corresponding non-Kummer case when q ≡ 2 (mod 3) and I will explain why this setting is somewhat easier to handle than the Kummer case when q ≡ 1 (mod 3), which allows us to prove some better results.