Difference sets and shifted primes

被引：15
作者：
Lucier, J. [1 ]
机构：
[1] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada
来源：
ACTA MATHEMATICA HUNGARICA | 2008年 / 120卷 / 1-2期
关键词：
Hardy-Littlewood method; difference sets; shifted primes;
D O I：
10.1007/s10474-007-7107-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that if A is a subset of {1,..., n} which has no pair of elements whose difference is equal to p -1 with p a prime nuniber, then the size of A is O(n (log log n) (-c( log log log log n))) for some absolute c > 0.
引用
收藏
页码：79 / 102
页数：24
相关论文
共 13 条
[1]   DIFFERENCE SETS WITHOUT KAPPA-TH POWERS [J].
BALOG, A ;
PELIKAN, J ;
PINTZ, J ;
SZEMEREDI, E .
ACTA MATHEMATICA HUNGARICA, 1994, 65 (02) :165-187
[2]   ERGODIC BEHAVIOR OF DIAGONAL MEASURES AND A THEOREM OF SZEMEREDI ON ARITHMETIC PROGRESSIONS [J].
FURSTENBERG, H .
JOURNAL D ANALYSE MATHEMATIQUE, 1977, 31 :204-256
[3]   A new proof of Szemeredi's theorem [J].
Gowers, WT .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2001, 11 (03) :465-588
[4]   On arithmetic structures in dense sets of integers [J].
Green, B .
DUKE MATHEMATICAL JOURNAL, 2002, 114 (02) :215-238
[5]  
Halberstam H., 1974, SIEVE METHODS, V4
[6]  
Hardy G. H., 1979, INTRO THEORY NUMBERS
[7]   VANDER CORPUT DIFFERENCE THEOREM [J].
KAMAE, T ;
FRANCE, MM .
ISRAEL JOURNAL OF MATHEMATICS, 1978, 31 (3-4) :335-342
[8]   Intersective sets given by a polynomial [J].
Lucier, Jason .
ACTA ARITHMETICA, 2006, 123 (01) :57-95
[9]  
MONTGOMERY HL, 1971, LECT NOTES MATH, V127
[10]  
PINTZ J, 1988, J LOND MATH SOC, V37, P219
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