Geodesics and commensurability classes of arithmetic hyperbolic $3$ -manifolds
Chinburg, T. ; Hamilton, E. ; Long, D. D. ; Reid, A. W.
Duke Math. J., Tome 141 (2008) no. 1, p. 25-44 / Harvested from Project Euclid
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We show that if $M$ is an arithmetic hyperbolic $3$ -manifold, the set $\mathbb{Q}L(M)$ 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
Publié le : 2008-10-01
Classification:  53C22,  58J53,  11R42 
@article{1221656861,
     author = {Chinburg, T. and Hamilton, E. and Long, D. D. and Reid, A. W.},
     title = {Geodesics and commensurability classes of arithmetic hyperbolic $3$ -manifolds},
     journal = {Duke Math. J.},
     volume = {141},
     number = {1},
     year = {2008},
     pages = { 25-44},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1221656861}
}

Chinburg, T.; Hamilton, E.; Long, D. D.; Reid, A. W. Geodesics and commensurability classes of arithmetic hyperbolic $3$ -manifolds. Duke Math. J., Tome 141 (2008) no. 1, pp.  25-44. http://gdmltest.u-ga.fr/item/1221656861/