A generalization of furstenberg's diophantine theorem

Bryna Kra*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We obtain a generalization of Furstenberg's Diophantino Theorem on non-lacunary multiplicative semigroups. For example we show that the sets of sums {(p1nq1m + P2nq2m)α : n,m ε ℕ} and {(p1nq1m + 2n)α : n,m ε ℕ} are dense in the circle = ℝ/ℤ for all irrational α, where (pi,qi;) are distinct pairs of multiplicatively independent integers for i = 1,2.

Original languageEnglish (US)
Pages (from-to)1951-1956
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number7
StatePublished - 1999


  • Distribution modulo
  • Topological dynamics

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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