Additive Correlation and the Inverse Problem for the Large Sieve

@article{Hanson2017AdditiveCA,
  title={Additive Correlation and the Inverse Problem for the Large Sieve},
  author={B. Hanson},
  journal={arXiv: Number Theory},
  year={2017},
  pages={1-7}
}
  • B. Hanson
  • Published 2017
  • Mathematics
  • arXiv: Number Theory
  • Let $A\subset [1,N]$ be a set of positive integers with $|A|\gg \sqrt N$. We show that if avoids about $p/2$ residue classes modulo $p$ for each prime $p$, the $A$ must correlate additively with the squares $S=\{n^2:1\leq n\leq \sqrt N\}$, in the sense that we have the additive energy estimate $E(A,S)\gg N\log N$. This is, in a sense, optimal. 

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