{"paper":{"title":"Spectra of lens spaces from 1-norm spectra of congruence lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT","math.SP"],"primary_cat":"math.DG","authors_text":"Emilio A. Lauret, Juan Pablo Rossetti, Roberto J. Miatello","submitted_at":"2013-11-27T21:58:51Z","abstract_excerpt":"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 (resp.\\ isospectral on $p$-forms for every $p$) if and only if the associated congruence lattices are $\\|\\cdot\\|_1$-isospectral (resp.\\ $\\|\\cdot\\|_1$-isospectral plus a geometric condition). Using this fact, we give, for every dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7167","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}