{"paper":{"title":"Relative Trace Formula, Subconvexity and Quantitative Nonvanishing of Rankin-Selberg $L$-functions for $\\mathrm{GL}(n+1)\\times\\mathrm{GL}(n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liyang Yang","submitted_at":"2023-09-14T09:00:15Z","abstract_excerpt":"Let $\\pi'$ be a fixed unitary cuspidal representation of $\\mathrm{GL}(n)/\\mathbb{Q}.$ We establish a subconvex bound in the $t$-aspect\n  $$ L(1/2+it,\\pi\\times\\pi')\\ll_{\\pi,\\pi',\\varepsilon}(1+|t|)^{\\frac{n(n+1)}{4}-\\frac{1}{4\\cdot (4n^2+2n-1)}+\\varepsilon}, \n$$ for any unitary pure isobaric automorphic representation $\\pi$ of $\\mathrm{GL}(n+1)/\\mathbb{Q}.$ Moreover, the bound improves in the standard $L$-function case $$ L(1/2+it, \\pi')\\ll_{\\pi',\\varepsilon}(1+|t|)^{\\frac{n}{4}-\\frac{1}{4(n+1)(4n-1)}+\\varepsilon}. $$\n  We also prove an explicit lower bound for nonvanishing of central $L$-value"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.07534","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.07534/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}