Dynamics of geodesics, and Maass cusp forms
Abstract
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We surveyin a way intended to be accessible to a wide audience of mathematiciansa mathematically rigorous instance of such a relation that emerged in recent years, showing a dynamical interpretation of certain Laplace eigenfunctions of hyperbolic surfaces.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 DOI:
 10.48550/arXiv.1906.01067
 arXiv:
 arXiv:1906.01067
 Bibcode:
 2019arXiv190601067P
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Number Theory;
 Mathematics  Spectral Theory;
 11F37;
 11F67;
 37D40;
 37D35;
 37B10
 EPrint:
 30 pages, 17 figures