Abstract
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
Citation
T. Chinburg. E. Hamilton. D. D. Long. A. W. Reid. "Geodesics and commensurability classes of arithmetic hyperbolic -manifolds." Duke Math. J. 145 (1) 25 - 44, 1 October 2008. https://doi.org/10.1215/00127094-2008-045
Information