Duke Mathematical Journal
- Duke Math. J.
- Volume 145, Number 1 (2008), 25-44.
Geodesics and commensurability classes of arithmetic hyperbolic -manifolds
We show that if is an arithmetic hyperbolic -manifold, the set of all rational multiples of lengths of closed geodesics of both determines and is determined by the commensurability class of . This implies that the spectrum of the Laplace operator of determines the commensurability class of . We also show that the zeta function of a number field with exactly one complex place determines the isomorphism class of the number field
Duke Math. J., Volume 145, Number 1 (2008), 25-44.
First available in Project Euclid: 17 September 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Chinburg, T.; Hamilton, E.; Long, D. D.; Reid, A. W. Geodesics and commensurability classes of arithmetic hyperbolic $3$ -manifolds. Duke Math. J. 145 (2008), no. 1, 25--44. doi:10.1215/00127094-2008-045. https://projecteuclid.org/euclid.dmj/1221656861