The limit points of the bass notes of arithmetic hyperbolic surfaces

TL;DR

This paper establishes that the set of limit points for the bass notes of arithmetic hyperbolic surfaces forms a continuous interval from 0 to 1/4, revealing a fundamental spectral property.

Contribution

It proves that the limit points of the bass notes of arithmetic hyperbolic surfaces fill the entire interval [0, 1/4], a new spectral result in hyperbolic geometry.

Findings

Limit points of bass notes form the interval [0, 1/4]

Spectral properties of arithmetic hyperbolic surfaces

Continuous spectrum of bass notes

Abstract

We prove that the limit points of the bass notes of arithmetic hyperbolic surfaces are the interval $\left[0,\frac{1}{4}\right]$.