Gergely Harcos

(Alfréd Rényi Institute of Mathematics)

Equidistribution on the modular surface and automorphic L-functions

According to a great discovery of Lagrange there are only finitely many integral binary quadratic forms of given nonzero discriminant up to equivalence, that is, every such form can be reduced by some invertible integral substitution to one of finitely many forms. Depending on the sign of the discriminant the equivalence classes give rise to special points or closed geodesics on a certain hyperbolic surface, and the distribution of these objects have deep arithmetic content. In my lecture I will try to highlight some of the exciting moments of this old new story.