MIT Number Theory Seminar

Wanlin Li (MIT)

Title: “Vanishing of Hyperelliptic L-functions at the Central Point”

Abstract: We study the number of quadratic Dirichlet L-functions over the rational function field which vanish at the central point s=1/2. In the first part of my talk, I will give a lower bound on the number of such characters through a geometric interpretation. This is in contrast with the situation over the rational numbers, where a conjecture of Chowla predicts there should be no such L-functions. In the second part of the talk, I will discuss joint work with Ellenberg and Shusterman proving as the size of the constant field grows to infinity, the set of quadratic L-functions vanishing at the central point has 0 density.