{"paper":{"title":"Conjecture and improved extension theorems for paraboloids in the finite field setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Doowon Koh","submitted_at":"2016-03-21T17:43:17Z","abstract_excerpt":"We study the extension estimates for paraboloids in d-dimensional vector spaces over finite fields F_q with q elements. We use the connection between L^2 based restriction estimates and L^p\\to L^r extension estimates for paraboloids. As a consequence, we improve the L^2\\to L^r extension results obtained by A. Lewko and M. Lewko in even dimensions d\\ge 6 and odd dimensions d=4\\ell+3 for \\ell \\in \\mathbb N. Our results extend the consequences for 3-D paraboloids due to M. Lewko to higher dimensions. We also clarifies conjectures on finite field extension problems for paraboloids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06512","kind":"arxiv","version":4},"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"}