{"paper":{"title":"Poincar\\'e series for non-Riemannian locally symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GR","math.MP","math.SP"],"primary_cat":"math.RT","authors_text":"Fanny Kassel, Toshiyuki Kobayashi","submitted_at":"2012-09-18T19:57:17Z","abstract_excerpt":"The discrete spectrum of the Laplacian has been extensively studied on reductive symmetric spaces and on Riemannian locally symmetric spaces. Here we examine it for the first time in the general setting of non-Riemannian, reductive, locally symmetric spaces.\n  For any non-Riemannian, reductive symmetric space X on which the discrete spectrum of the Laplacian is nonempty, and for any discrete group of isometries Gamma whose action on X is sufficiently proper, we construct L^2-eigenfunctions of the Laplacian on X_{Gamma}:=Gamma\\X for an infinite set of eigenvalues. These eigenfunctions are obtai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4075","kind":"arxiv","version":2},"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"}