Non-vanishing of L-functions over function fields (Alexandra Florea, UC Irvine)

I will talk about some results concerning the non-vanishing of $L$-functions associated to fixed order characters $\ell$ at the central point over functions fields. Quadratic characters have been studied a lot over the years, and very good non-vanishing results are available in this case, due to work of Soundararajan. When focusing on cubic and higher order characters, much less is known. In this talk, I will explain how one can obtain a positive proportion of non-vanishing for any fixed order $\ell$ characters, which goes to $0$ as $\ell$ goes to infinity. This is based on joint work with C. David and M. Lalin.