Marios Voskou

Hyperbolic Counting Problems

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 space. We will explain why these problems are much harder and interpret them in terms of the distribution of arithmetic objects such as sums of four squares and norms of ideals in number fields. Furthermore, we study refined distribution questions (i.e. equidistribution) relating to the work of A.Good. We use automorphic forms and their analytic theory.