{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:EJRVEGLDSX7FOKSY7NR2IADZ4K","short_pith_number":"pith:EJRVEGLD","schema_version":"1.0","canonical_sha256":"226352196395fe572a58fb63a40079e2bcecd5e5deb979aab785b4487a28160f","source":{"kind":"arxiv","id":"2309.07534","version":1},"attestation_state":"computed","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 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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 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