The Fourier Restriction and Kakeya Problems over Rings of Integers Modulo N

被引：10

作者：

Hickman, Jonathan ^{[1
]}

Wright, James ^{[2
]}

机构：

[1] Univ Chicago, Dept Math, Eckhart Hall Room 414,5734 S Univ Ave, Chicago, IL 60637 USA

[2] Room 4621,James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland

来源：

DISCRETE ANALYSIS | 2018年

基金：

美国国家科学基金会;

关键词：

Fourier restriction; Kakeya; Congruence equations; EXTENSION-THEOREMS; RECENT PROGRESS; VECTOR-SPACES; FINITE; SETS; CURVES; CONJECTURES; TRANSFORMS; FAMILIES; SURFACES;

D O I：

10.19086/da.3682

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1 / 54

页数：54

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