On a theorem of Sarkozy for difference sets and shifted primes

被引：7

作者：

Wang, Ruoyi ^{[1
]}

机构：

[1] Univ Oxford, Math Inst, Radcliffe Observ Quarter,Woodstock Rd, Oxford OX2 6GG, England

来源：

JOURNAL OF NUMBER THEORY | 2020年 / 211卷

关键词：

Difference sets; Prime numbers; Hardy-Littlewood method; SEQUENCES;

D O I：

10.1016/j.jnt.2019.10.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that if the difference of two elements of a set A subset of [N] is never one less than a prime number, then vertical bar A vertical bar = O(N exp(-c(log N)(1/3))) for some absolute constant c > 0. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：220 / 234

页数：15

共 7 条

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[3]

PINTZ J, 1988, J LOND MATH SOC, V37, P219

[4] Difference sets and the primes [J].

Ruzsa, Imre Z. ;

Sanders, Tom .

ACTA ARITHMETICA, 2008, 131 (03) :281-301

[5] DIFFERENCE SETS OF SEQUENCES OF INTEGERS .1. [J].

SARKOZY, A .

ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1978, 31 (1-2) :125-149

[6] DIFFERENCE SETS OF SEQUENCES OF INTEGERS .3. [J].

SARKOZY, A .

ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1978, 31 (3-4) :355-386

[7]

Sarkozy A., 1979, ANN U SCI BUDAP, V21, P45

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