On finite addition theorems

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

If a finite set A of integers included in {1 , . . . , N} has more than N/k elements, one may expect that the set ℓA of sums of ℓ elements of A, contains, when ℓ is comparable to k, a rather long arithmetic progression (which can be required to be homogeneous or not). After presenting the state of the art, we show that some of the results cannot be improved as far as it would be thought possible in view of the known results in the infinite case. The paper ends with lower and upper bounds for the order, as asymptotic bases, of the subsequences of the primes which have a positive relative density.

Original languageEnglish
Pages (from-to)109-127
Number of pages19
JournalAsterisque
Volume258
Publication statusPublished - Dec 1 1999

Keywords

  • Additive bases
  • Additive number theory
  • Density
  • Structure theory of set addition

ASJC Scopus subject areas

  • Mathematics(all)

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