# Some Relations between Spectral Geometry and Number Theory

#### Abstract

In his paper Mc], whose object was to show that the spectrum of the Laplacian of a Riemannian surface S determines the surface up to nitely many possibilities , Henry McKean proved the following result, which he called the \Riemann hypothesis for Riemann surfaces": Theorem (McKean Mc]). If S is a hyperbolic Riemann surface, then the rst eigenvalue 1 (S) of… (More)

### Cite this paper

@inproceedings{Brooks1992SomeRB, title={Some Relations between Spectral Geometry and Number Theory}, author={Robert Brooks}, year={1992} }