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math.NT2011
A new proof of Sarkozy's theorem
Neil Lyall
It is a striking and elegant fact (proved independently by Furstenberg and Sarkozy) that in any subset of the natural numbers of positive upper density there necessarily exist two…
math.NT2011
Polynomial Differences in the Primes
Neil Lyall, Alex Rice
We establish, utilizing the Hardy-Littlewood Circle Method, an asymptotic formula for the number of pairs of primes whose differences lie in the image of a fixed polynomial. We als…