无l形构型的子集

IF 1.3 1区数学 Q1 MATHEMATICS

Compositio Mathematica Pub Date : 2023-12-04 DOI:10.1112/s0010437x2300756x

Sarah Peluse

引用次数: 0

摘要

修复一个质数$p\geq 11$。我们证明了存在一个正整数$m$，使得$\mathbb {F}_p^n\times \mathbb {F}_p^n$的任何子集不包含$(x,y)$, $(x,y+z)$, $(x,y+2z)$, $(x+z,y)$的非寻常配置必须具有密度$\ll 1/\log _{m}{n}$，其中$\log _{m}$表示$m$ -fold迭代对数。本文给出了二维四点位形在任意情况下的多维szemersamedi定理的第一个合理界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Subsets of without L-shaped configurations

Fix a prime $p\geq 11$. We show that there exists a positive integer $m$ such that any subset of $\mathbb {F}_p^n\times \mathbb {F}_p^n$ containing no nontrivial configurations of the form $(x,y)$, $(x,y+z)$, $(x,y+2z)$, $(x+z,y)$ must have density $\ll 1/\log _{m}{n}$, where $\log _{m}$ denotes the $m$-fold iterated logarithm. This gives the first reasonable bound in the multidimensional Szemerédi theorem for a two-dimensional four-point configuration in any setting.

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来源期刊

Compositio Mathematica 数学-数学

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Compositio Mathematica is a prestigious, well-established journal publishing first-class research papers that traditionally focus on the mainstream of pure mathematics. Compositio Mathematica has a broad scope which includes the fields of algebra, number theory, topology, algebraic and differential geometry and global analysis. Papers on other topics are welcome if they are of broad interest. All contributions are required to meet high standards of quality and originality. The Journal has an international editorial board reflected in the journal content.