A POLYNOMIAL ROTH THEOREM FOR CORNERS IN FINITE FIELDS

被引：5

作者：

Han, Rui ^{[1
]}

Lacey, Michael T. ^{[2
]}

Yang, Fan ^{[2
]}

机构：

[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

MATHEMATIKA | 2021年 / 67卷 / 04期

基金：

美国国家科学基金会;

关键词：

11B30; (primary);

D O I：

10.1112/mtk.12108

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a Roth-type theorem for polynomial corners in the finite field setting. Let phi(1) and phi(2) be two polynomials of distinct degree. For sufficiently large primes p, any subset A subset of FpxFp with |A|>p2-116 contains three points (x1,x2),(x1+phi 1(y),x2),(x1,x2+phi 2(y)). The study of these questions on Fp was started by Bourgain and Chang. Our Theorem adapts the argument of Dong, Li, and Sawin, in particular relying upon deep Weil-type inequalities established by N. Katz.

引用

页码：885 / 896

页数：12

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