{"paper":{"title":"Growth Estimates in Positive Characteristic via Collisions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendan Murphy, Esen Aksoy Yazici, Ilya Shkredov, Misha Rudnev","submitted_at":"2015-12-21T13:12:24Z","abstract_excerpt":"Let $F$ be a field of characteristic $p>2$ and $A\\subset F$ have sufficiently small cardinality in terms of $p$. We improve the state of the art of a variety of sum-product type inequalities. In particular, we prove that $$ |AA|^2|A+A|^3 \\gg |A|^6,\\qquad |A(A+A)|\\gg |A|^{3/2}. $$ We also prove several two-variable extractor estimates: ${\\displaystyle |A(A+1)| \\gg|A|^{9/8},}$ $$ |A+A^2|\\gg |A|^{11/10},\\; |A+A^3|\\gg |A|^{29/28}, \\; |A+1/A|\\gg |A|^{31/30}.$$\n  Besides, we address questions of cardinalities $|A+A|$ vs $|f(A)+f(A)|$, for a polynomial $f$, where we establish the inequalities $$ \\max"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06613","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"}