{"paper":{"title":"Slightly improved sum-product estimates in fields of prime order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Liangpan Li","submitted_at":"2009-07-12T19:28:58Z","abstract_excerpt":"Let $\\mathbb{F}_p$ be the field of residue classes modulo a prime number $p$ and let $A$ be a nonempty subset of $\\mathbb{F}_p$. In this paper we show that if $|A|\\preceq p^{0.5}$, then \\[ \\max\\{|A\\pm A|,|AA|\\}\\succeq|A|^{13/12};\\] if $|A|\\succeq p^{0.5}$, then \\[ \\max\\{|A\\pm A|,|AA|\\}\\succapprox \\min\\{|A|^{13/12}(\\frac{|A|}{p^{0.5}})^{1/12},|A|(\\frac{p}{|A|})^{1/11}\\}.\\] These results slightly improve the estimates of Bourgain-Garaev and Shen. Sum-product estimates on different sets are also considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2051","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0907.2051/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}