Abstract
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 language | English (US) |
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Pages (from-to) | 1951-1956 |
Number of pages | 6 |
Journal | Proceedings of the American Mathematical Society |
Volume | 127 |
Issue number | 7 |
DOIs | |
State | Published - 1999 |
Keywords
- Distribution modulo
- Topological dynamics
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics