A generalization of furstenberg's diophantine theorem

Bryna Kra

doi:10.1090/s0002-9939-99-04742-5

A generalization of furstenberg's diophantine theorem

Bryna Kra^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We obtain a generalization of Furstenberg's Diophantino Theorem on non-lacunary multiplicative semigroups. For example we show that the sets of sums {(p₁ⁿq₁^m + P₂ⁿq₂^m)α : n,m ε ℕ} and {(p₁ⁿq₁^m + 2ⁿ)α : n,m ε ℕ} are dense in the circle = ℝ/ℤ for all irrational α, where (p_i,q_i;) are distinct pairs of multiplicatively independent integers for i = 1,2.

Original language	English (US)
Pages (from-to)	1951-1956
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	127
Issue number	7
DOIs	https://doi.org/10.1090/s0002-9939-99-04742-5
State	Published - 1999

Keywords

Distribution modulo
Topological dynamics

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0002-9939-99-04742-5

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title = "A generalization of furstenberg's diophantine theorem",

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.",

keywords = "Distribution modulo, Topological dynamics",

author = "Bryna Kra",

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T1 - A generalization of furstenberg's diophantine theorem

AU - Kra, Bryna

PY - 1999

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N2 - 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.

AB - 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.

KW - Distribution modulo

KW - Topological dynamics

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VL - 127

SP - 1951

EP - 1956

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 7

ER -

A generalization of furstenberg's diophantine theorem

Abstract

Keywords

ASJC Scopus subject areas

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