Spectral Distribution of Twisted Laplacian on Typical Hyperbolic Surfaces of High Genus

Abstract

We investigate the spectral distribution of the twisted Laplacian associated with uniform square-integrable bounded harmonic 1-form on typical hyperbolic surfaces of high genus. First, we estimate the spectral distribution by the supremum norm of the corresponding harmonic form. Subsequently, we show that the square-integrable bounded harmonic form exhibits a small supremum norm for typical hyperbolic surfaces of high genus. Based on these findings, we prove a uniform Weyl law for the distribution of real parts of the spectrum on typical hyperbolic surfaces.

References in corpus (4)

• Random hyperbolic surfaces of large genus have first eigenvalues greater than $\frac{3}{16}-\epsilon$
• Twisted Ruelle zeta function at zero for compact hyperbolic surfaces
• Optimal lower bounds for first eigenvalues of Riemann surfaces for large genus
• Spectral convergence of the Dirac operator on typical hyperbolic surfaces of high genus

Cited by in corpus (2)

• Spectral convergence of the Dirac operator on typical hyperbolic surfaces of high genus
• Averages of determinants of Laplacians over moduli spaces for large genus