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- W3098477758 abstract "To every |$n$|-dimensional lens space |$L$|, we associate a congruence lattice |$mathcal L$| in |$mathbb {Z}^m$|, with |$n=2m-1$| and we prove a formula relating the multiplicities of Hodge–Laplace eigenvalues on |$L$| with the number of lattice elements of a given |$|{cdot }|_1$|-length in |$mathcal L$|. As a consequence, we show that two lens spaces are isospectral on functions (respectively, isospectral on |$p$|-forms for every |$p$|) if and only if the associated congruence lattices are |$|{cdot }|_1$|-isospectral (respectively, |$|{cdot }|_1$|-isospectral plus a geometric condition). Using this fact, we give, for every dimension |$nge 5$|, infinitely many examples of Riemannian manifolds that are isospectral on every level |$p$| and are not strongly isospectral." @default.
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- W3098477758 date "2015-06-04" @default.
- W3098477758 modified "2023-09-30" @default.
- W3098477758 title "Spectra of Lens Spaces from 1-Norm Spectra of Congruence Lattices" @default.
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- W3098477758 doi "https://doi.org/10.1093/imrn/rnv159" @default.
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