Nonvanishing of L-functions of fixed order characters over function fields

We present some results concerning the non-vanishing of L-functions associated with fixed order characters at the central point over functions fields. More specifically, we will explain how one can compute the one-level density of zeros in a thin family of such L-functions and obtain a positive proportion of non-vanishing, which goes to 0 as the order of the character goes to infinity. This is based on joint work with C. Bujold, C. David, and A. Florea.

Matilde Lalin is an Argentinian-Canadian mathematician. She completed her undergraduate studies at the Universidad de Buenos Aires, obtained her doctorate at the University of Texas at Austin, and was a postdoctoral researcher at the Institute for Advanced Study and PIMS-UBC, where she inhabited office WMAX 113 between 2006 and 2007. After a brief stint as an assistant professor at the University of Alberta, she moved to the Université de Montréal, where she is currently a full professor and a CRM Distinguished Scholar. She received the Krieger-Nelson Prize in 2022 and is a Fellow of the CMS, the AMS, and the AWM. She has been involved with BIRS in various capacities for 10 years, which has given her perfect excuses to continue visiting the UBC campus and occasionally enjoying the Mathematics building.