Additive correlation and the inverse problem for the large sieve

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Let A [1, N] be a set of integers with |A| ≫. We show that if A avoids about p/2 residue classes modulo p for each prime p, then A must correlate additively with the squares S = {n2 : 1 ≤ n ≤ }, in the sense that we have the additive energy estimate This is, in a sense, optimal.

Original languageEnglish (US)
Pages (from-to)211-217
Number of pages7
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number2
Publication statusPublished - Mar 1 2020


All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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