ARITHMETIC PROGRESSIONS IN SETS OF FRACTIONAL DIMENSION

被引：59

作者：

Laba, Izabella ^{[1
]}

Pramanik, Malabika ^{[1
]}

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2009年 / 19卷 / 02期

关键词：

Arithmetic progressions; Salem sets; Hausdorff dimension; restriction estimates; SALEM SETS; THEOREM; CONSTRUCTION; PRIMES; ERDOS;

D O I：

10.1007/s00039-009-0003-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E subset of R be a closed set of Hausdorff dimension alpha. We prove that if a is sufficiently close to 1, and if E supports a probability measure obeying appropriate dimensionality and Fourier decay conditions, then E contains non-trivial 3-term arithmetic progressions.

引用

页码：429 / 456

页数：28

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