Abstract
We study additive intersective properties of sparse subsets of integers. In particular, we prove that for every set S with counting function o(log n) there exists a set A with lower asymptotic density 1/2 such that A + A is disjoint from S. We also show that this result is best possible.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alon N., Kolountzakis M.: On a problem of Erdös and Turán and some related results. J. Number Theory 55, 82–93 (1995)
Alon N., Spencer J.: The Probabilistic Method. Wiley, New York (2000)
Graham R.L., Rothschild B. L., Spencer J.: Ramsey theory. Wiley, New York (1990)
Guy R.: Unsolved problems in number theory. Springer-Verlag, New York (1994)
Halberstam H., Roth K.F.: Sequences. Springer-Verlag, New York-Berlin (1983)
Author information
Authors and Affiliations
Corresponding author
Additional information
Research partially supported by MNSW Grant 2 P03A 029 30.
Rights and permissions
About this article
Cite this article
Schoen, T. Sum-intersective sets. Arch. Math. 94, 219–226 (2010). https://doi.org/10.1007/s00013-009-0097-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-009-0097-1