Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

13^th  of December 2023, 16:00-17:00, room 2001

 

 

 

 

 

 

 

 

 On Chowla's non vanishing conjecture

 

Carlo Pagano
Concordia University

 

 

 

I will describe ongoing work with Peter Koymans and Mark
Shusterman, showing that for fixed q congruent to 3 modulo 4, one has
non-vanishing of L(1/2,chi) for 100% of imaginary quadratic characters chi
of Fq(T) (ordered by discriminant). This result, predicted by the
Katz-Sarnak heuristics, is the probabilistic version of Chowla's non
vanishing conjecture: it is known that over function fields one cannot hope
for a deterministic statement, as shown in a fairly robust way by Wanlin Li
in 2018. I will explain how this result sits into a web of methods aimed at
controlling the distribution of 2^{infty}-Selmer groups in quadratic twists
families.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry