Heidi Goodson : Sato-Tate groups of trinomial hyperelliptic curves

Posted by Alina Carmen Cojocaru , part of the Number Theory Seminar.

At

Nov. 8, 2019, 9:30 a.m.

In

1227 SEO

Abstract

Let $C_m: y^2=x^m+c$ be a smooth projective curve defined over $\mathbb Q$. We would like to study the limiting distributions of the coefficients of the normalized L-polynomial for $C_m$. To determine the distributions, we study the Sato-Tate groups of the Jacobians of the curves. In this talk, I will give both general results and explicit examples of Sato-Tate groups for certain curves $C_m$. I will then use these groups to determine the limiting distributions of the coefficients of the normalized L-polynomial. This is joint work with M. Emory.

The seminar lasts 80 minutes (9:30am-10:50am).