Number Theory Seminar
Heidi Goodson
Brooklyn College, CUNY, Brooklyn, NY
Sato-Tate groups of trinomial hyperelliptic curves
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).
Friday November 8, 2019 at 9:30 AM in 1227 SEO