Congruence obstructions to pseudomodularity of Fricke groups

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dc.creatorFithian, David
dc.date2007-07-28
dc.date2007-07-31
dc.date.accessioned2026-07-07T08:20:55Z
dc.date.available2026-07-07T08:20:55Z
dc.descriptionA pseudomodular group is a finite coarea nonarithmetic Fuchsian group whose cusp set is exactly $\mathbb{P}^1(\mathbb{Q})$. Long and Reid constructed finitely many of these by considering Fricke groups, i.e., those that uniformize one-cusped tori. We prove that a zonal Fricke group with rational cusps is pseudomodular if and only if its cusp set is dense in the finite adeles of $\mathbb{Q}$. We then deduce that infinitely many such Fricke groups are not pseudomodular.
dc.description4 pages
dc.identifierhttps://arxiv.org/abs/0707.4261
dc.identifierhttp://arxiv.org/abs/0707.4261
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/135210
dc.subjectNumber Theory
dc.subject20H10
dc.titleCongruence obstructions to pseudomodularity of Fricke groups
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