Abstract
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| ≥ N1/3−c, 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 language | English |
---|---|
Pages (from-to) | 1167-1191 |
Number of pages | 25 |
Journal | American Journal of Mathematics |
Volume | 138 |
Issue number | 5 |
DOIs | |
State | Published - Oct 2016 |
Bibliographical note
Publisher Copyright:© 2016 by Johns Hopkins University Press.
ASJC Scopus subject areas
- General Mathematics