Manin's conjecture for Châtelet surfaces

Algebraic Geometry and Number Theory Seminar

We resolve Manin's conjecture for all Chtelet surfaces over 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.