A new upper bound for sets with no square differences

2020/11/26 by Thomas F. Bloom, Bloom, Thomas F., James E. Maynard +1 · 3 citations
Mathematics · #11B30 #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2011.13266

openalex publication_date 2020/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We show that if A⊂ \1,…,N\ has no solutions to a-b=n² with a,b∈ 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-Szemerédi.

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• Some Mizohata-Takeuchi-type estimate for exponential sums
• Furstenberg--Sárközy theorem over number fields
• Notes and computations on forbidden differences

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