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The limit points of the bass notes of arithmetic hyperbolic surfaces

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arxiv 2403.00928 v2 pith:X5A2LTE2 submitted 2024-03-01 math.NT math.APmath.DGmath.PRmath.SP

Michael Magee This is my paper · ORCID
classification math.NTmath.APmath.DGmath.PRmath.SP
keywords arithmeticbasshyperboliclimitnotespointssurfacesfrac
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abstract

We prove that the limit points of the bass notes of arithmetic hyperbolic surfaces are the interval $\left[0,\frac{1}{4}\right]$.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Spectral gaps on thick part of moduli spaces

    math.DG 2025-01 conditional novelty 7.0 of 10

    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→∞.

  2. Limit points of uniform arithmetic bass notes

    math.SP 2024-12 conditional novelty 7.0 of 10

    For closed arithmetic hyperbolic surfaces, the possible values of the first nonzero Laplace eigenvalue form a dense subset of [0, 1/4].

  3. Bass notes of random hyperbolic surfaces of large genus

    math.SP 2026-07 accept novelty 2.0 of 10

    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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