Conditional on GRH for quadratic L-functions, proves explicit uniform spectral gap for Laplacian on X_0(p) covers of Schottky surfaces X when limit set is thick enough.
Soares, Improved fractal weyl bounds for convex cocompact hyperbol ic surfaces and large resonance-free regions, (2023), arXiv preprint: 2301.03023
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Explicit spectral gap for Hecke congruence covers of arithmetic Schottky surfaces
Conditional on GRH for quadratic L-functions, proves explicit uniform spectral gap for Laplacian on X_0(p) covers of Schottky surfaces X when limit set is thick enough.