{"paper":{"title":"The Burgess bound via a trivial delta method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Keshav Aggarwal, Qingfeng Sun, Roman Holowinsky, Yongxiao Lin","submitted_at":"2018-03-01T18:23:32Z","abstract_excerpt":"Let $g$ be a fixed Hecke cusp form for $\\mathrm{SL}(2,\\mathbb{Z})$ and $\\chi$ be a primitive Dirichlet character of conductor $M$. The best known subconvex bound for $L(1/2,g\\otimes \\chi)$ is of Burgess strength. The bound was proved by a couple of methods: shifted convolution sums and the Petersson/Kuznetsov formula analysis. It is natural to ask what inputs are really needed to prove a Burgess-type bound on $\\rm GL(2)$. In this paper, we give a new proof of the Burgess-type bounds ${L(1/2,g\\otimes \\chi)\\ll_{g,\\varepsilon} M^{1/2-1/8+\\varepsilon}}$ and $L(1/2,\\chi)\\ll_{\\varepsilon} M^{1/4-1/1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00542","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1803.00542/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"}