## Number Theory - Chantal David (Concordia University)

### Tuesday, April 23nrd, 2019

**Time:** 1:30-2:30 p.m. **Place:** Jeffery Hall 319

**Speaker:** Chantal David (Concordia University)

**Title:** Moments of cubic Dirichlet twists over function fields (Joint work with A. Florea and M. Lalin.)

**Abstract:** We obtain an asymptotic formula for the mean value of $L$--functions associated to cubic characters over $\F_q[T]$. We solve this problem in the non-Kummer setting when $q \equiv 2 \pmod 3$ and in the Kummer case when $q \equiv 1 \pmod 3$. The proofs rely on evaluating averages of cubic Gauss sums over function fields, which can be done using the theory of metaplectic Eisenstein series. In the non-Kummer setting, we display some explicit cancellation between the main term and the dual term coming from the approximate functional equation of the $L$--functions.