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Spectral gaps on thick part of moduli spaces
Published 16 Jan 2025 in math.DG, math.CV, math.GT, math.NT, and math.SP | (2501.09266v1)
Abstract: In this paper, we study spectral gaps of closed hyperbolic surfaces for large genus. We show that for any fixed $k\geq 1$, as the genus goes to infinity, the maximum of $\lambda_k-\lambda_{k-1}$ over any thick part of the moduli space of closed Riemann surfaces approaches the limit $\frac{1}{4}$.
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