Difference sets and the primes
arXiv:0710.0644 · doi: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.
19 pp. Corrected typos. Updated references.
Cited by in corpus (6)
- On a theorem of Sárközy for difference sets and shifted primes
- A Maximal Extension of the Best-Known Bounds for the Furstenberg-Sárközy Theorem
- An explicit version of Bombieri's log-free density estimate and Sárközy's theorem for shifted primes
- On improving a Schur-type theorem in shifted primes
- A quantitative bound on Furstenberg-Sárközy patterns with shifted prime power common differences in primes
- Multivariate Polynomial Values in Difference Sets