A new upper bound for sets with no square differences

DOI10.1112/S0010437X22007679OpenAlexW3109240484MaRDI QIDQ5041007

James Maynard, Thomas F. Bloom

Publication date: 18 October 2022

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.13266

zbMATH Keywords

squaresdifference setadditive combinatoricsdensity increment

Mathematics Subject Classification ID

Applications of the Hardy-Littlewood method (11P55) Quadratic and bilinear Diophantine equations (11D09) Arithmetic combinatorics; higher degree uniformity (11B30)

Cites Work

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• Difference sets without \(\kappa\)-th powers
• A polynomial bound in Freiman's theorem.
• Simultaneous small fractional parts of polynomials
• An improved lower bound related to the Furstenberg-Sárközy theorem
• Mean and large values of Dirichlet polynomials
• Sárközy's Theorem in Function Fields
• On Sets of Natural Numbers Whose Difference Set Contains No Squares
• On difference sets of sequences of integers. I
• A maximal extension of the best-known bounds for the Furstenberg–Sárközy theorem
• Breaking the k ² barrier for explicit RIP matrices
• Difference sets and the primes

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