1 results
On Selberg’s eigenvalue conjecture for moduli spaces of abelian differentials
- Part of
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- Journal:
- Compositio Mathematica / Volume 155 / Issue 12 / December 2019
- Published online by Cambridge University Press:
- 30 October 2019, pp. 2354-2398
- Print publication:
- December 2019
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- Article
- Export citation
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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
$\frac{3}{16}$ theorem to moduli spaces of abelian differentials on surfaces of genus 
${\geqslant}2$.
