{"paper":{"title":"Congruence properties of induced representations and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexei Venkov, Arash Momeni, Dieter Mayer","submitted_at":"2012-10-22T17:37:34Z","abstract_excerpt":"In this paper we study congruence properties of the representations $U_\\alpha:=U^{PSL(2,\\mathbb{Z})}_{\\chi_\\alpha}$ of the projective modular group ${\\rm PSL}(2,\\mathbb{Z})$ induced from a family $\\chi_\\alpha$ of characters for the Hecke congruence subgroup $\\Gamma_0(4)$ basically introduced by A. Selberg. Interest in the representations $U_\\alpha$ stems from their appearance in the transfer operator approach to Selberg's zeta function for this Fuchsian group and character $\\chi_\\alpha$. Hence the location of the nontrivial zeros of this function and therefore also the spectral properties of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5979","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"}