Year: 2026
Type: preprint
Abstract: We study sign bias between hyperbolic double cosets with $ad>0$ and $ad<0$ in appropriate cocompact Fuchsian groups. We prove that an eventual bias can only favour $ad<0$, and show that such a bias occurs within every cocompact Fuchsian commensurability class. When the normal-derivative periods of all nonconstant eigenfunctions with eigenvalue at most $1/4$ vanish, we prove an $Ω_\pm(X^{1/2})$ result and show that the counting difference takes both signs in every sufficiently large interval $[X,CX]$, for some fixed $C>1$.
Source: arXiv (Cornell University)
Author: Voskou, Marios
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223021901