A refinement of strong multiplicity one for spectra of hyperbolic manifolds

2011/08/15 by Kelmer, Dubi · 2 citations
#11F72 #22E45 #FOS: Mathematics #Number Theory (math.NT) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1108.2977

Abstract

Let \calM₁ and \calM₂ denote two compact hyperbolic manifolds. Assume that the multiplicities of eigenvalues of the Laplacian acting on L²(\calM₁) and L²(\calM₂) (respectively, multiplicities of lengths of closed geodesics in \calM₁ and \calM₂) 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 iso-spectral.

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