{"paper":{"title":"Finite field restriction estimates for the paraboloid in high even dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alex Iosevich, Doowon Koh, Mark Lewko","submitted_at":"2017-12-15T06:07:58Z","abstract_excerpt":"We prove that the finite field Fourier extension operator for the paraboloid is bounded from $L^2\\to L^r$ for $r\\geq \\frac{2d+4}{d}$ in even dimensions $d\\ge 8$, which is the optimal $L^2$ estimate. For $d=6$ we obtain the optimal range $r> \\frac{2d+4}{d}=8/3$, apart from the endpoint. For $d=4$ we improve the prior range of $r>16/5=3.2$ to $r\\geq 28/9=3.111\\ldots$, compared to the conjectured range of $r\\geq3$. The key new ingredient is improved additive energy estimates for subsets of the paraboloid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05549","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":""},"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"}