Difference sets and the primes

Imre Z. Ruzsa, Tom Sanders

Type: Article

Publication Date: 2008-01-01

Citations: 20

DOI: https://doi.org/10.4064/aa131-3-5

Abstract

Suppose that A is a subset of {1,...,N} such that the difference between any two elements of A is never one less than a prime. We show that |A| = O(N exp(-c(log N)^{1/4})) for some absolute c>0.

Locations

Acta Arithmetica - View - PDF
arXiv (Cornell University) - View - PDF
DataCite API - View

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Works Cited by This (7)

Action	Title	Year	Authors
+	Integer sets containing no arithmetic progressions	1990	Endre Szemerédi
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+	On Sets of Natural Numbers Whose Difference Set Contains No Squares	1988	J. Pintz William Steiger Endre Szemerédi
+	On measures of intersectivity	1984	Imre Z. Ruzsa
+	Integer Sets Containing No Arithmetic Progressions	1987	D. R. Heath‐Brown
+	Multiplicative Number Theory I: Classical Theory	2006	Hugh L. Montgomery R. C. Vaughan
+	MULTIPLICATIVE NUMBER THEORY	1970	Enrico Bombieri