On a theorem of Sárközy for difference sets and shifted primes

Abstract

We show that if the difference of two elements of a set $A\subseteq [N]$ is never one less than a prime number, then $|A|=O(N\exp (-c(\log N{)}^{1/3}))$ for some absolute constant $c>0$.

arXiv commentTitle changed. Referee comments incorporated

References in corpus (1)

• Difference sets and the primes

Cited by in corpus (5)

• An explicit version of Bombieri's log-free density estimate and Sárközy's theorem for shifted primes
• Lower bounds in the polynomial Szemerédi theorem
• 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