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arXiv · 2610.26462

Sign bias in hyperbolic double cosets

Marios Voskou
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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 construct examples exhibiting such a bias. 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 $C>1$.

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BibTeXRIS

Marios Voskou. 2026-10-19. Sign bias in hyperbolic double cosets. https://arxiv.org/abs/2610.26462

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