{"paper":{"title":"On a spectral analogue of the strong multiplicity one theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Chandrasheel Bhagwat, C.S. Rajan","submitted_at":"2010-09-03T15:07:57Z","abstract_excerpt":"We prove spectral analogues of the classical strong multiplicity one theorem for newforms. Let $\\Gamma_1$ and $\\Gamma_2$ be uniform lattices in a semisimple group $G$. Suppose all but finitely many irreducible unitary representations (resp. spherical) of $G$ occur with equal multiplicities in $L^{2}(\\Gamma_1 \\backslash G)$ and $L^{2}(\\Gamma_2 \\backslash G)$. Then $L^{2}(\\Gamma_1 \\backslash G) \\cong L^{2}(\\Gamma_2 \\backslash G)$ as $G$ - modules (resp. the spherical spectra of $L^{2}(\\Gamma_1 \\backslash G)$ and $L^{2}(\\Gamma_2 \\backslash G)$ are equal)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0694","kind":"arxiv","version":1},"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"}