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PreprintCC BY 4.0arXiv

Resonance counting and spectral gaps for hyperbolic surfaces via Fourier decay

  • Louis Soares
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Abstract

We prove an improved fractal Weyl upper bound for resonances of infinite-area convex cocompact hyperbolic surfaces, expressed in terms of the Hausdorff dimension of the limit set and the Fourier decay exponent of the Patterson--Sullivan measure. This bound also yields a sharper upper bound for the essential spectral gap for these surfaces.

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Cite

BibTeXRIS
BibTeX
@misc{soares2026resonance,
  title = {{Resonance counting and spectral gaps for hyperbolic surfaces via Fourier decay}},
  author = {Louis Soares},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17276},
  eprint = {2610.17276},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17276},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Resonance counting and spectral gaps for hyperbolic surfaces via Fourier decay
AU  - Louis Soares
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17276
UR  - https://arxiv.org/abs/2610.17276
AB  - We prove an improved fractal Weyl upper bound for resonances of infinite-area convex cocompact hyperbolic surfaces, expressed in terms of the Hausdorff dimension of the limit set and the Fourier decay exponent of the Patterson--Sullivan measure. This bound also yields a sharper upper bound for the essential spectral gap for these surfaces.
ER  -