{"paper":{"title":"Non-vanishing of Maass form L-functions at the critical point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anders S\\\"odergren, Bingrong Huang, Olga Balkanova","submitted_at":"2018-10-18T11:23:35Z","abstract_excerpt":"In this paper, we consider the family $\\{L_j(s)\\}_{j=1}^{\\infty}$ of $L$-functions associated to an orthonormal basis $\\{u_j\\}_{j=1}^{\\infty}$ of even Hecke-Maass forms for the modular group $SL(2, Z)$ with eigenvalues $\\{\\lambda_j=\\kappa_{j}^{2}+1/4\\}_{j=1}^{\\infty}$. We prove the following effective non-vanishing result: At least $50 \\%$ of the central values $L_j(1/2)$ with $\\kappa_j \\leq T$ do not vanish as $T\\rightarrow \\infty$. Furthermore, we establish effective non-vanishing results in short intervals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07991","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"}