Joint Number theory/Geometry and analysis seminar
Speaker: Niko Laaksonen UCL visiting KU
Title: Lattice Point Counting in Sectors of Hyperbolic Space
Abstract: Huber demonstrated how the hyperbolic lattice point problem in conjugacy classes corresponds to counting lattice points in a sector of the hyperbolic plane.
This is equivalent to counting geodesic segments according to length. For this problem, Good and Chatzakos--Petridis proved separately an error term analogous to that of Selberg.
We show how this generalises to three dimensions and prove a similar strong bound on the error term. We will also apply the work of Chamizo on large sieve inequalities in hyperbolic spaces to our problem in the radial and spatial aspects. In particular, we will discuss why these yield diminishing returns in higher dimensions.