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

Published online by Cambridge University Press:  30 October 2019

Michael Magee
Department of Mathematical Sciences, Durham University, Lower Mountjoy, Stockton Rd, Durham DH1 3LE, UK email


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 ${\geqslant}2$ .

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