A sum-product estimate in finite fields,and applications期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

A sum-product estimate in finite fields,and applications

Authors:	Jean Bourgain Nets Katz Terence Tao

Institution:	(1) School of Mathematics, Institute of Advanced Study, Princeton, NJ 08540, USA;(2) Department of Mathematics, Washington University in St. Louis, St. Louis, MO 63130, USA;(3) Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA

Abstract:	Let A be a subset of a finite field $F := \mathbf{Z}/q\mathbf{Z}$ for some prime q. If $\|F\|^{\delta} < \|A\| < \|F\|^{1-\delta}$ for some > 0, then we prove the estimate $\|A + A\| + \|A \cdot A\| \geq c(\delta)\|A\|^{1+\varepsilon}$ for some = () > 0. This is a finite field analogue of a result of ErS]. We then use this estimate to prove a Szemerédi-Trotter type theorem in finite fields, and obtain a new estimate for the Erdös distance problem in finite fields, as well as the three-dimensional Kakeya problem in finite fields.

Keywords:	((no ))
本文献已被 SpringerLink 等数据库收录！