{"paper":{"title":"L-functions and sharp resonances of infinite index congruence subgroups of $SL_2(\\mathbb{Z})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Dmitry Jakobson, Frederic Naud","submitted_at":"2017-04-27T13:04:00Z","abstract_excerpt":"For convex co-compact subgroups of SL2(Z) we consider the \"congruence subgroups\" for p prime. We prove a factorization formula for the Selberg zeta function in term of L-functions related to irreducible representations of the Galois group SL2(Fp) of the covering, together with a priori bounds and analytic continuation. We use this factorization property combined with an averaging technique over representations to prove a new existence result of non-trivial resonances in an effective low frequency strip."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08546","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"}