Philadelphia Area Number Theory Seminar

Wednesday, December 4, 2019 - 2:15pm

Heidi Goodson

Brooklyn College (CUNY)

Let Cm : y2 = xm + c be a smooth projective curve defined over Q. We would like to study the limiting distributions of the coefficients of the normalized L-polynomial for Cm. 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 Cm. 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.