On an inverse ternary Goldbach problem

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We prove an inverse ternary Goldbach-type result. Let N be sufficiently large and c >0 be sufficiently small. If A1, A2, A3 ⊂ [N] are subsets with |A1|, |A2|, |A3| ≥ N1/3c, then A1+ A2+ A3 contains a composite number. This improves on the bound N1/3+o(1) obtained by using Gallagher’s larger sieve. The main ingredients in our argument include a type of inverse sieve result in the larger sieve regime, and a variant of the analytic large sieve inequality.

Original languageEnglish
Pages (from-to)1167-1191
Number of pages25
JournalAmerican Journal of Mathematics
Issue number5
StatePublished - Oct 2016

Bibliographical note

Publisher Copyright:
© 2016 by Johns Hopkins University Press.

ASJC Scopus subject areas

  • General Mathematics


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