{"paper":{"title":"Subconvexity for $GL(1)$ twists of Rankin-Selberg $L$-functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aritra Ghosh","submitted_at":"2023-03-16T20:57:25Z","abstract_excerpt":"Let $f$ and $g$ be two holomorphic or Hecke-Maass primitive cusp forms for $SL(2,\\mathbb{Z})$ and $\\chi$ be a primitive Dirichlet character of modulus $p$, an odd prime. A subconvex bound for the central values of the Rankin-Selberg $L$-functions is $L(s, f \\otimes g \\otimes \\chi)$ is given by $$L(\\frac{1}{2}, f \\otimes g \\otimes \\chi) \\ll_{f,g,\\epsilon}p^{\\frac{27}{28}+\\epsilon} ,$$ for any $\\epsilon > 0$, where the implied constant depends only on the forms $f,g$ and $\\epsilon$. Here the convexity bound has exponent $1+\\epsilon$, which was improved to $1-\\frac{1}{1324}$ (see \\cite{HM}). Our "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.09646","kind":"arxiv","version":5},"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/2303.09646/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"}