Seminars
Tue, 03 Mar 2026
16:00
16:00
L6
The hyperbolic lattice point problem
Stephen Lester
Abstract
In this talk I will discuss the hyperbolic circle problem for $SL_2(\mathbb Z)$. Given two points $z, w$ that lie in the hyperbolic upper half‑plane, the problem is to determine the number of $SL_2(\mathbb Z)$ translates of w that lie in the hyperbolic disk centred at z with radius $arcosh(R/2)$ for large $R$. Selberg proved that the error term in this problem is $O(R^{2/3})$. I will describe some recent work in which we improve the error term to $o(R^{2/3})$ as $R$ tends to infinity, for $z,w$ that are CM-points of different, square-free discriminants. This is joint work with Dimitrios Chatzakos, Giacomo Cherubini, and Morten Risager.