Papers › Spectrum of the Laplacian on the Fricke-Macbeath surface
Spectrum of the Laplacian on the Fricke-Macbeath surface
Chul-hee Lee
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The Fricke-Macbeath surface is the unique Hurwitz surface of genus 7 with 504 conformal automorphisms. In this paper, we prove that the first eigenvalue of the Laplacian on the Fricke-Macbeath surface has a sevenfold multiplicity and contained in the interval [1.23, 1.26]. Further, we numerically identify the 7-dimensional representation of its automorphism group corresponding to the eigenspace associated to the first eigenvalue. We also determine the Dirichlet domain centered at 0 for a Fuchsian group that uniformizes the Fricke-Macbeath surface, identifying the algebraic coordinates for its vertices.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections