L-functions in Analytic Number Theory: Wanlin Li

A Dirichlet character over Fq(t) corresponds to a curve over Fq. Using this connection to geometry, we construct families of characters whose L-functions vanish (resp. does not vanish) at the central point. The existence of infinitely many vanishing L-functions is in contrast with the situation over the rational numbers, where a conjecture of Chowla predicts there should be no such. Towards Chowla's conjecture, for each fixed q, we present an explicit upper bound on the number of such quadratic characters which decreases as q grows and it goes to 0 percent as q goes to infinity. In this talk, I will also discuss phenomena and interesting questions related to this problem. Some results in this talk are from projects joint with Ravi Donepudi, Jordan Ellenberg and Mark Shusterman.

This event is part of the PIMS CRG Group on L-Functions in Analytic Number Theory. More details can be found on the webpage here: https://sites.google.com/view/crgl-functions/crg-weekly-seminar?authuser=0