English

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 316\frac{3}{16} Theorem to moduli spaces of abelian differentials on surfaces of genus 2\geq 2.

Keywords

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

R2 v1 2026-06-22T15:53:25.923Z