Number Theory Days in Lille

The mean value of cubic L-functions over function fields

8 juil. 2019, 14:00

1h

Salle de réunion (Université de Lille)

Analytic-additive number theory

Orateur

Matilde Lalín (Université de Montréal)

Description

We present results about the first moment of L-functions associated to cubic characters over ${\mathbb{F}}_q(T)$ when q is congruent to 1 modulo 3. The case of number fields was considered in previous work, but never for the full family of cubic twists over a field containing the third roots of unity. We will explain how to obtain an asymptotic formula with a main term, which relies on using results from the theory of metaplectic Eisenstein series about cancellation in averages of cubic Gauss sums over functions fields. We will also discuss the case q congruent to 2 modulo 3.