{"paper":{"title":"Discrete restriction estimates of epsilon-removal type for kth-powers and k-paraboloids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CO"],"primary_cat":"math.NT","authors_text":"Kevin Henriot, Kevin Hughes","submitted_at":"2016-10-13T09:04:37Z","abstract_excerpt":"We obtain restriction estimates of $\\epsilon$-removal type for the set of $k$-th powers of integers, and for discrete $d$-dimensional surfaces of the form \\[ \\{ (n_1,\\dots,n_d,n_1^k + \\dotsb + n_d^k) \\,:\\, |n_1|,\\dots,|n_d| \\leq N \\}, \\] which we term '$k$-paraboloids'. For these surfaces, we obtain a satisfying range of exponents for large values of $d,k$. We also obtain estimates of $\\epsilon$-removal type in the full supercritical range for $k$-th powers and for $k$-paraboloids of dimension $d < k(k-2)$. We rely on a variety of techniques in discrete harmonic analysis originating in Bourgai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03984","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"}