Vortrag am

Donnerstag, 25.6.2015

Morten Risager, Kopenhagen

"The hyperbolic circle problem "


Abstract: The circle problem seeks to estimate the number of points of an orbit Gz inside a disc of growing radius R, where G acts discontinuously on a metric space X. When X is the plane and G is the standard lattice this is the classical Gauss circle problem. This is a long and well-studied problem, with precise conjectures and strong results. The hyperbolic circle problem concerns hyperbolic plane and groups like SL(2,Z) acting on it. This case seems much harder and the best known error estimates are in a precise sense - which we will explain - much weaker. We will explore different averages of arithmetic significance which improves on the error terms. We will also report on a work in progress trying to improve the error term for z certain Heegner points.