Limit points of uniform arithmetic bass notes

TL;DR

This paper establishes that the accumulation points of spectral gaps in closed arithmetic hyperbolic surfaces fill the entire interval from 0 to 1/4, revealing a comprehensive spectral property of these surfaces.

Contribution

It proves that the set of limit points of spectral gaps for closed arithmetic hyperbolic surfaces is exactly the interval [0, 1/4], a new result in spectral geometry.

Findings

Limit points of spectral gaps form the interval [0, 1/4]

Spectral gaps are densely accumulated in this interval

The result characterizes the spectral distribution of these surfaces

Abstract

We prove that the set of limit points of the set of all spectral gaps of closed arithmetic hyperbolic surfaces equals $[0,\frac{1}{4}]$.