A refinement of strong multiplicity one for spectra of hyperbolic manifolds

Let \calM_1 and \calM_2 denote two compact hyperbolic manifolds. Assume that the multiplicities of eigenvalues of the Laplacian acting on L^2(\calM_1) and L^2(\calM_2) (respectively, multiplicities of lengths of closed geodesics in \calM_1 and \calM_2) are the same, except for a possibly infinite exceptional set of eigenvalues (respectively lengths). We define... Show more