Algebra and Number Theory Seminar: Twisted Moments of Dirichlet L-functions in Function Fields

Abstract: The study of moments of Dirichlet L-functions is an important topic to study due to its applications with the Lindelöf hypothesis and non-vanishing results. In this talk, we will study the twisted second moments of Dirichlet L-functions in function fields with one and two twists, when averaged over primitive Dirichlet characters of modulus R, where R is a monic polynomial in Fq[T]. As an application, we will discuss how these asymptotic formulas can be used to obtain non-vanishing results for these Dirichlet L-functions at the central point. This is a joint work with Julio Andrade.