A geometric characterization of arithmetic Fuchsian groups

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dc.creatorGeninska, S.
dc.creatorLeuzinger, E.
dc.date2006-09-17
dc.date.accessioned2026-07-07T09:50:32Z
dc.date.available2026-07-07T09:50:32Z
dc.descriptionThe trace set of a Fuchsian group $Γ$ ist the set of length of closed geodesics in the surface $Γ\backslash \mathbb{H}$. Luo and Sarnak showed that the trace set of a cofinite arithmetic Fuchsian group satisfies the bounded clustering property. Sarnak then conjectured that the B-C property actually characterizes arithmetic Fuchsian groups. Schmutz stated the even stronger conjecture that a cofinite Fuchsian group is arithmetic if its trace set has linear growth. He proposed a proof of this conjecture in the case when the group $Γ$ contains at least one parabolic element, but unfortunately this proof contains a gap. In the present paper we point out this gap and we prove Sarnak's conjecture under the assumption that the Fuchsian group $Γ$ contains parabolic elements.
dc.description23 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0609477
dc.identifierhttp://arxiv.org/abs/math/0609477
dc.identifierDuke Math. J. 142 (2008), 111-125
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164971
dc.subjectDifferential Geometry
dc.subjectGroup Theory
dc.subject20H10, 30F35, 11F06, 22E40
dc.titleA geometric characterization of arithmetic Fuchsian groups
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