{"paper":{"title":"An effective bound for the Huber constant for cofinite Fuchsian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.NT","authors_text":"Jay Jorgenson, Joshua S. Friedman, Jurg Kramer","submitted_at":"2010-03-08T15:23:33Z","abstract_excerpt":"Let $\\Gamma$ be a cofinite Fuchsian group acting on hyperbolic two-space $\\HH.$ Let $M=\\Gamma \\setminus \\HH $ be  the corresponding quotient space. For $\\gamma,$ a closed geodesic of $M$, let $l(\\gamma)$ denote its length. The prime geodesic counting function $\\pi_{M}(u)$ is defined as the number of $\\Gamma$-inconjugate, primitive, closed geodesics $\\gamma $  such that $e^{l(\\gamma)} \\leq u.$ The \\emph{prime geodesic theorem} implies:\n $$\\pi_{M}(u)=\\sum_{0 \\leq \\lambda_{M,j} \\leq 1/4} \\text{li}(u^{s_{M,j}}) + O_{M}(\\frac{u^{3/4}}{\\log{u}}), $$ where $0=\\lambda_{M,0} < \\lambda_{M,1} <...$ are t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1652","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"}