# On a theorem of Sárközy for difference sets and shifted primes

@article{Wang2020OnAT,
title={On a theorem of S{\'a}rk{\"o}zy for difference sets and shifted primes},
author={Ruoyi Wang},
journal={Journal of Number Theory},
year={2020}
}
• R. Wang
• Published 8 June 2019
• Mathematics
• Journal of Number Theory
Multivariate Polynomial Values in Difference Sets
• Mathematics, Computer Science
• 2020
Every set lacking nonzero differences in $h(\mathbb{Z}^{\ell}) satisfies certain nonsingularity conditions, provided$h ($h) contains a multiple of every natural number and$h$satisfies certain nontingingularity conditions. A quantitative bound on Furstenberg-S\'ark\"ozy patterns with shifted prime power common differences in primes Let k > 1 be a fixed integer, and PN be the set of primes no more than N . We prove that if set A ⊂ PN contains no patterns p1, p1 + (p2 − 1), where p1, p2 are prime numbers, then |A| |PN | ≪ ( log On improving a Schur-type theorem in shifted primes We show that if N ≥ exp(exp(exp(k))), then any k-colouring of the primes that are less than N contains a monochromatic solution to p1 − p2 = p3 − 1. Quantitative bounds for Gowers uniformity of the M\"obius and von Mangoldt functions • Mathematics • 2021 We establish quantitative bounds on the U[N ] Gowers norms of the Möbius function μ and the von Mangoldt function Λ for all k, with error terms of shapeO((log logN)−c). As a consequence, we obtain ## References SHOWING 1-6 OF 6 REFERENCES Difference sets and the primes • Mathematics • 2008 Suppose that A is a subset of {1,...,N} such that the difference between any two elements of A is never one less than a prime. We show that |A| = O(N exp(-c(log N)^{1/4})) for some absolute c>0. Difference sets and shifted primes We show that if A is a subset of {1, …, n} which has no pair of elements whose difference is equal to p − 1 with p a prime number, then the size of A is O(n(log log n)−c(log log log log log n)) for Analytic Number Theory • Mathematics • 2004 Introduction Arithmetic functions Elementary theory of prime numbers Characters Summation formulas Classical analytic theory of$L\$-functions Elementary sieve methods Bilinear forms and the large
On sets of natural numbers whose difference set contains no squares
• Mathematics
• 1988
We show that if a sequence s/ of natural numbers has no pair of elements whose difference is a positive square, then the density of J/ n{l,...,«} is O(l/log«) c »), cn->-oo. This improves previous