A fundamental domain of Ford type for $SO(3,Z[i])\backslash SO(3,C)/SO(3)$, and for $SO(2,1)_Z\backslash SO(2,1)/SO(2)$

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dc.creatorBrenner, Eliot
dc.date2006-04-29
dc.date2006-11-22
dc.date.accessioned2026-07-07T07:13:47Z
dc.date.available2026-07-07T07:13:47Z
dc.descriptionLet $G=SO(3,C)$, $Γ=SO(3,Z[i])$, $K=SO(3)$, and let $X$ be the locally symmetric space $Γ\backslash G/K$. In this paper, we write down explicit equations defining a fundamental domain for the action of $Γ$ on $G/K$. The fundamental domain is well-adapted for studying the theory of $Γ$-invariant functions on $G/K$. We write down equations defining a fundamental domain for the subgroup $Γ_Z=SO(2,1)_Z$ of $Γ$ acting on the symmetric space $G_{R}/K_R$, where $G_R$ is the split real form SO(2,1) of $G$ and $K_R$ is its maximal compact subgroup SO(2). We formulate a simple geometric relation between the fundamental domain of $Γ$ and $Γ_Z$ so described. These fundamental domains are geared towards the detailed study of the spectral theory of $X$ and the embedded subspace $X_R=Γ_Z\backslash G_R/K_R$.}
dc.description30 pages. Article gives summary of main results of the e-print math.NT/0605012, with addition of background information and motivation. Submitted to the Israel Journal of Mathematics
dc.identifierhttps://arxiv.org/abs/math/0605013
dc.identifierhttp://arxiv.org/abs/math/0605013
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112606
dc.subjectNumber Theory
dc.subject11F55 (Primary), 11F72, 11H55 (Secondary)
dc.titleA fundamental domain of Ford type for $SO(3,Z[i])\backslash SO(3,C)/SO(3)$, and for $SO(2,1)_Z\backslash SO(2,1)/SO(2)$
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