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A Spectral Gap for Spinors on Hyperbolic Surfaces

Number Theory 2025-06-23 v1 Differential Geometry Spectral Theory

Abstract

The purpose of this note is to construct a sequence of spin hyperbolic surfaces Σn\Sigma_n with genus going to infinity and with a uniform spectral gap for the Dirac operator. Our construction is completely explicit. In particular, the Σn\Sigma_n can be taken to be a tower of covers, with each Σn\Sigma_n an arithmetic hyperbolic surface.

Keywords

Cite

@article{arxiv.2506.17092,
  title  = {A Spectral Gap for Spinors on Hyperbolic Surfaces},
  author = {Anshul Adve and Vikram Giri},
  journal= {arXiv preprint arXiv:2506.17092},
  year   = {2025}
}

Comments

13 pages, comments welcome!

R2 v1 2026-07-01T03:26:47.191Z