An application of the sum-product phenomenon to sets avoiding several linear equations

被引：3

作者：

Shkredov, I. D. ^{[1
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Moscow, Russia

来源：

SBORNIK MATHEMATICS | 2018年 / 209卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

additive combinatorics; sum-product; Fourier transform;

D O I：

10.1070/SM8907

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the theory of sum-products we prove that for an arbitrary k <= 1/3 any subset of F-p avoiding t linear equations with three variables has size less than O(p/t(k)).

引用

页码：580 / 603

页数：24

共 35 条

[31] Decomposition of homogenous differential linear expression that are a product of symbolic factors and relative application to the study of linear differential equations.
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[32] USE OF LINEAR NONSYMMETRIC EIGENVALUE EQUATIONS FOR A SUM-OVER-POINTS APPROACH - APPLICATION TO H2+
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[35] THE DISCRETIZATION OF CONTINUOUS INFINITE SETS OF COUPLED ORDINARY LINEAR-DIFFERENTIAL EQUATIONS - APPLICATION TO THE COLLISION-INDUCED DISSOCIATION OF A DIATOMIC MOLECULE BY AN ATOM
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