On Selberg’s eigenvalue conjecture for moduli spaces of abelian differentials

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 g...

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Bibliographic Details
Published in:Compositio mathematica 2019-12, Vol.155 (12), p.2354-2398
Main Author: Magee, Michael
Format: Article
Language:English
Subjects:
Eigenvalues
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Summary: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 ${\geqslant}2$ .
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X1900767X