{"paper":{"title":"A sum-product theorem in function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Thomas Bloom, Timothy G. F. Jones","submitted_at":"2012-11-23T13:07:29Z","abstract_excerpt":"Let $A$ be a finite subset of $\\ffield$, the field of Laurent series in $1/t$ over a finite field $\\mathbb{F}_q$. We show that for any $\\epsilon>0$ there exists a constant $C$ dependent only on $\\epsilon$ and $q$ such that $\\max\\{|A+A|,|AA|\\}\\geq C |A|^{6/5-\\epsilon}$. In particular such a result is obtained for the rational function field $\\mathbb{F}_q(t)$. Identical results are also obtained for finite subsets of the $p$-adic field $\\mathbb{Q}_p$ for any prime $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5493","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"}