Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Number Theory Seminar


Tuesday, September 10th, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Seoyoung Kim (Queen's University)

Title: The Sato-Tate conjecture and Nagao’s conjecture.

Abstract: Nagao’s conjecture relates the rank of an elliptic surface to a limit formula arising from a weighted average of fibral Frobenius traces, and it is further generalized for smooth irreducible projective surfaces by Hindry and Pacheco. We show that the Sato-Tate conjecture for abelian surfaces studied by Fit\'{e}, Kedlaya, Rotger, Sutherland implies Nagao’s conjecture for certain twist families hyperelliptic curves of genus 2. Moreover, one can relate analogous discussions for higher genus g to the non-vanishing result on the symmetric power $L$-functions, from which analogous proof will hold for certain cases.