A new upper bound for sets with no square differences

2022/08/01 by Thomas F. Bloom, James Maynard · 5 citations
Mathematics · #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Point processes and geometric inequalities

paper · doi:10.1112/s0010437x22007679

Abstract

We show that if \mathcal A⊂ \1,…,N\ has no solutions to a-b=n² with a,b∈ \mathcal A and n≥ 1 , then | A| ≪ \fracN(log N)^{cloglog log N} for some absolute constant c>0 . This improves upon a result of Pintz, Steiger, and Szemerédi.

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