{"paper":{"title":"On the fields generated by the lengths of closed geodesics in locally symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.DG","authors_text":"Andrei S. Rapinchuk, Gopal Prasad","submitted_at":"2011-10-02T00:02:28Z","abstract_excerpt":"This paper is the next installment of our analysis of length-commensurable locally symmetric spaces begun in Publ. math. IHES 109(2009), 113-184. For a Riemannian manifold $M$, we let $L(M)$ be the weak length spectrum of $M$, i.e. the set of lengths of all closed geodesics in $M$, and let $\\mathcal{F}(M)$ denote the subfield of $\\mathbb{R}$ generated by $L(M)$. Let now $M_i$ be an arithmetically defined locally symmetric space associated with a simple algebraic $\\mathbb{R}$-group $G_i$ for $i = 1, 2$. Assuming Schanuel's conjecture from transcendental number theory, we prove (under some minor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0141","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"}