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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A refinement of strong multiplicity one for spectra of hyperbolic manifolds


Author: Dubi Kelmer
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 11F72; Secondary 58J53, 22E45
Published electronically: March 13, 2014
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Abstract: Let $ \mathcal {M}_1$ and $ \mathcal {M}_2$ denote two compact hyperbolic manifolds. Assume that the multiplicities of eigenvalues of the Laplacian acting on $ L^2(\mathcal {M}_1)$ and $ L^2(\mathcal {M}_2)$ (respectively, multiplicities of lengths of closed geodesics in $ \mathcal {M}_1$ and $ \mathcal {M}_2$) are the same, except for a possibly infinite exceptional set of eigenvalues (respectively lengths). We define a notion of density for the exceptional set and show that if it is below a certain threshold, the two manifolds must be isospectral.


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Additional Information

Dubi Kelmer
Affiliation: Department of Mathematics, 301 Carney Hall, Boston College, Chestnut Hill, Massachusetts 02467
Email: dubi.kelmer@bc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06102-3
PII: S 0002-9947(2014)06102-3
Received by editor(s): February 20, 2012
Received by editor(s) in revised form: January 23, 2013
Published electronically: March 13, 2014
Additional Notes: This work was partially supported by NSF grant DMS-1001640
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.