{"paper":{"title":"A log-free zero-density estimate and small gaps in coefficients of $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Amir Akbary, Timothy S. Trudgian","submitted_at":"2013-12-20T06:25:45Z","abstract_excerpt":"Let $L(s, \\pi\\times\\pi^\\prime)$ be the Rankin--Selberg $L$-function attached to automorphic representations $\\pi$ and $\\pi^\\prime$. Let $\\tilde{\\pi}$ and $\\tilde{\\pi}^\\prime$ denote the contragredient representations associated to $\\pi$ and $\\pi^\\prime$. Under the assumption of certain upper bounds for coefficients of the logarithmic derivatives of $L(s, \\pi\\times\\tilde{\\pi})$ and $L(s, \\pi^\\prime\\times\\tilde{\\pi}^\\prime)$, we prove a log-free zero-density estimate for $L(s, \\pi\\times\\pi^\\prime)$ which generalises a result due to Fogels in the context of Dirichlet $L$-functions. We then employ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5820","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"}