Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows

Livio Flaminio; Davide Ravotti

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arXiv · 2207.08263

Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows

Livio Flaminio·Davide Ravotti

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Abstract

We consider Abelian covers of compact hyperbolic surfaces. We establish an asymptotic expansion of the correlations for the horocycle flow on $\mathbb{Z}^d$-covers, thus proving a strong form of Krickeberg mixing. We also prove that the spectral measures around $0$ of the Casimir operators on any increasing sequence of finite Abelian covers converge weakly to an absolutely continuous measure.

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Livio Flaminio, Davide Ravotti. 2022-07-17. Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows. https://arxiv.org/abs/2207.08263

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