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The limit points of the bass notes of arithmetic hyperbolic surfaces
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abstract
We prove that the limit points of the bass notes of arithmetic hyperbolic surfaces are the interval $\left[0,\frac{1}{4}\right]$.
Forward citations
Cited by 5 Pith papers
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A Spectral Gap for Spinors on Hyperbolic Surfaces
An explicit tower of abelian covers of the genus-2 curve y^2=x^6-1 has Dirac operator spectral gap uniformly bounded below by a positive constant.
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Spectral gaps on thick part of moduli spaces
For every fixed k and every ε>0, the maximum of λ_k - λ_{k-1} over genus-g hyperbolic surfaces with systole at least ε tends to 1/4 as g→∞.
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Limit points of uniform arithmetic bass notes
For closed arithmetic hyperbolic surfaces, the possible values of the first nonzero Laplace eigenvalue form a dense subset of [0, 1/4].
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Spectral gap with polynomial rate for random covering surfaces
Random degree-n covers of a closed hyperbolic surface have no new Laplacian eigenvalues below 1/4 - c n^{-b} with probability tending to 1 as n grows.
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Bass notes of random hyperbolic surfaces of large genus
A survey of recent results proving that random hyperbolic surfaces of large genus have near-optimal spectral gaps, after Hide–Magee, Anantharaman–Monk, and Hide–Macera–Thomas.
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