On Selberg's Eigenvalue Conjecture for moduli spaces of abelian differentials
Dynamical Systems
2019-11-06 v4 Group Theory
Number Theory
Spectral Theory
Abstract
J.-C. Yoccoz proposed a natural extension of Selberg's Eigenvalue Conjecture to moduli spaces of abelian differentials. We prove an approximation to this conjecture. This gives a qualitative generalization of Selberg's Theorem to moduli spaces of abelian differentials on surfaces of genus .
Cite
@article{arxiv.1609.05500,
title = {On Selberg's Eigenvalue Conjecture for moduli spaces of abelian differentials},
author = {Michael Magee},
journal= {arXiv preprint arXiv:1609.05500},
year = {2019}
}
Comments
49 pages. Added section giving the Dolgopyat-type argument