Arithmetic lattices and weak spectral geometry

TL;DR

This paper discusses the relationship between arithmetic lattices and spectral geometry in hyperbolic spaces, providing insights into their mathematical structure and properties.

Contribution

It expands on three lectures to explore the connections between arithmetic lattices and weak spectral geometry in hyperbolic spaces.

Findings

Provides new theoretical insights into spectral properties of arithmetic lattices.

Connects hyperbolic geometry with arithmetic group theory.

Lays groundwork for future research in spectral geometry of hyperbolic spaces.

Abstract

This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.