Counting and Equidistribution in the Hyperbolic Plane — Marios Voskou (University College London)

In Euclidean space the Gauss’ Circle Problem is concerned with estimating the number of lattice points inside a Euclidean circle. In this talk we will discuss various analogous problems in the hyperbolic plane. We will explain why these problems are much harder and interpret them in terms of the distribution of arithmetic objects such as norms of ideals in number fields. Furthermore, we will study related refined distribution questions, such as equidistribution. We use automorphic forms and their spectral theory.