Manin's conjecture for Châtelet surfaces

Series
Athens-Atlanta Number Theory Seminar
Time
Tuesday, April 1, 2025 - 5:15pm for 1 hour (actually 50 minutes)
Location
Skiles 314
Speaker
Katherine Woo – Princeton University – khwoo@princeton.edu
Organizer
Alex Dunn

We resolve Manin's conjecture for all Châtelet surfaces over $\mathbb{Q}$ (surfaces given by equations of the form x^2 + ay^2 = f(z)) -- we establish asymptotics for the number of rational points of increasing height. The key analytic ingredient is estimating sums of Fourier coefficients of modular forms along polynomial values.