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Sign bias in hyperbolic double cosets
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±(X1/2) result and show that the counting difference takes both signs in every sufficiently large interval [X,CX], for some fixed C>1.
Related
- Dirichlet Beta Analogues, Sign Alternation, and Lerch Unification of Hyperbolic and Logarithmic Tangent Integrals
- Spectral gaps of double covers of hyperbolic surfaces
- Noncritical multi-bubbles and hyperbolic double bubbles
- Relativistic bound-state solutions for a non-central Schi{ö}berg-type hyperbolic potential with double ring-shaped angular terms
- Cosets with constant characteristic polynomial
BibTeX
@misc{voskou2026sign,
title = {{Sign bias in hyperbolic double cosets}},
author = {Marios Voskou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26462},
eprint = {2610.26462},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26462},
}
RIS
TY - UNPB
TI - Sign bias in hyperbolic double cosets
AU - Marios Voskou
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.26462
UR - https://arxiv.org/abs/2610.26462
AB - 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_±(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.
ER -