AN EXPLICIT INCIDENCE THEOREM IN Fp

被引：20

作者：

Helfgott, Harald Andres ^{[1
]}

Rudnev, Misha ^{[1
]}

机构：

[1] Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England

来源：

MATHEMATIKA | 2011年 / 57卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

SUM-PRODUCT ESTIMATE;

D O I：

10.1112/S0025579310001208

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let P = A x A subset of F-p x F-p, p a prime. Assume that P = A x A has n elements, n < p. See P as a set of points in the plane over F-p. We show that the pairs of points in P determine >= cn(1+1/267) lines, where c is an absolute constant. We derive from this an incidence theorem: the number of incidences between a set of n points and a set of n lines in the projective plane over F-p(n < p) is bounded by Cn(3/2-1/10678), where C is an absolute constant.

引用

页码：135 / 145

页数：11