The Fourier restriction and Kakeya problems over rings of integers modulo N

IF 1 3区数学 Q1 MATHEMATICS

Discrete Analysis Pub Date : 2018-01-09 DOI:10.19086/DA.3682

J. Hickman, James Wright

引用次数: 15

Abstract

The Fourier restriction phenomenon and the size of Kakeya sets are explored in the setting of the ring of integers modulo $N$ for general $N$ and a striking similarity with the corresponding euclidean problems is observed. One should contrast this with known results in the finite field setting.

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以N为模的整数环上的傅里叶限制和Kakeya问题

在一般N$的整数环模$N$的情况下，探讨了傅里叶限制现象和Kakeya集的大小，并观察到与相应的欧几里得问题的惊人相似性。我们应该将这与有限域的已知结果进行对比。

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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来源期刊

Discrete Analysis Mathematics-Algebra and Number Theory

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

17 weeks

期刊介绍： Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.