{"paper":{"title":"On the Odlyzko-Stanley enumeration problem and Waring's problem over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Jiyou Li","submitted_at":"2012-07-30T13:50:40Z","abstract_excerpt":"We obtain an asymptotic formula on the Odlyzko-Stanley enumeration problem.\nLet $N_m^*(k,b)$ be the number of $k$-subsets\n$S\\subseteq F_p^*$ such that $\\sum_{x\\in S}x^m=b$.\nIf $m<p^{1-\\delta}$, then there is a constant\n$\\epsilon=\\epsilon(\\delta)>0$ such that\n| N_m^*(k,b)-p^{-1}{p-1 \\choose k}|\\leq {p^{1-\\epsilon}+mk-m \\choose k}.\n  In addition, let $\\gamma'(m,p)$ denote the distinct Waring's number $(\\mod p)$, the smallest positive integer $k$ such that every integer is a sum of m-th powers of $k$-distinct elements $(\\mod p)$. The above bound implies that there is a constant $\\epsilon(\\delta)>"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6939","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"}