{"paper":{"title":"Averaging operators over nondegenerate quadratic surfaces in finite fields","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Doowon Koh","submitted_at":"2012-09-06T08:26:02Z","abstract_excerpt":"We study mapping properties of the averaging operator related to the variety $ V={x\\in \\mathbb F_q^d: Q(x)=0},$ where $Q(x)$ is a nondegenerate quadratic polynomial over a finite field $\\mathbb F_q$ with $q$ elements. This paper is devoted to eliminating the logarithmic bound appearing in the paper of Koh and Shen. As a consequence, we settle down the averaging problems over the quadratic surfaces $V$ in the case when the dimensions $d\\geq 4$ are even and $V$ contains a $d/2$-dimensional subspace."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1220","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":""},"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"}