Number Theory Seminar

Manin's conjecture for Châtelet surfaces

Katharine Woo, Postdoctoral Fellow, Department of Mathematics, Stanford University,

We resolve Manin's conjecture for all Châtelet 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.

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