By Dubi Kelmer and others

We answer in the affirmative a question of Sarnak's from 2007, confirming that the Patterson-Sullivan base eigenfunction is the unique square-integrable eigenfunction of the hyperbolic Laplacian invariant under the group of symmetries of the Apollonian packing. Thus the latter has a maximal spectral gap. We prove further restrictions on the... Show more

October 25, 2022

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Sarnak's spectral gap question

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