Thursday, April 1
Milner 216, 1:00 PM
Title: Hyperbolic distribution problems and indefinite quadratic forms
Abstract: Complex multiplication points play a central role in the study of number-theoretic properties of modular functions. We will show how to obtain equidistribution results for certain families of complex multiplication points, known as Heegner points, on Hilbert modular varieties. These results follow from subconvexity estimates for the Fourier coefficients of Hilbert-Maass forms by applying, amongst other things, techniques originated by Siegel (1944) and Maass (1949), together with certain "accidental isomorphisms" between orthogonal groups and modular groups. Our results generalize earlier work of Duke (1988) on the moduli space of elliptic curves. We also show that analogous results can be obtained in this way with the Heegner points replaced by families of varieties of positive dimension.