Geodesics and commensurability classes of arithmetic hyperbolic 3-manifolds

Ted Chinburg, Emily Hamilton, D. D. Long, Alan W. Reid

Type: Article

Publication Date: 2008-09-17

Citations: 50

DOI: https://doi.org/10.1215/00127094-2008-045

Abstract

We show that if M is an arithmetic hyperbolic 3-manifold, the set QL(M) of all rational multiples of lengths of closed geodesics of M both determines and is determined by the commensurability class of M. This implies that the spectrum of the Laplace operator of M determines the commensurability class of M. We also show that the zeta function of a number field with exactly one complex place determines the isomorphism class of the number field

Locations

Duke Mathematical Journal - View
CiteSeer X (The Pennsylvania State University) - View - PDF

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