ON THE POLYNOMIAL SZEMEREDI THEOREM IN FINITE FIELDS

被引：22
作者：
Peluse, Sarah [1 ]
机构：
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
来源：
DUKE MATHEMATICAL JOURNAL | 2019年 / 168卷 / 05期
基金：
美国国家科学基金会;
关键词：
DIFFERENCE SETS; PROGRESSIONS; SEQUENCES; PROOF;
D O I：
10.1215/00127094-2018-0051
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let P-1, . . . , P-m is an element of Z[y] be any linearly independent polynomials with zero constant term. We show that there exists gamma > 0 such that any subset of Fq of size at least q(1-gamma) contains a nontrivial polynomial progression x, x + P-1 (y), . . . , x + P-m (y), provided that the characteristic of F-q is large enough.
引用
收藏
页码：749 / 774
页数：26
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