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
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
