Algebraic numbers, hyperbolicity, and density modulo one

A. Gorodnik, S. Kadyrov

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We prove the density of the sets of the form{λ 1 mμ 1 nξ 1+...+λ k mμ k nξk:m,n∈N} modulo one, where λ i and μ i are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelian groups.

Original language English 2499-2509 11 Journal of Number Theory 132 11 https://doi.org/10.1016/j.jnt.2012.05.018 Published - Nov 2012 Yes

Algebraic number
Hyperbolicity
Compact Group
Abelian group
Modulo
Form

Keywords

• Compact abelian group
• Density modulo one
• Higher-rank abelian action
• Multiplicatively independent numbers

ASJC Scopus subject areas

• Algebra and Number Theory

Cite this

Algebraic numbers, hyperbolicity, and density modulo one. / Gorodnik, A.; Kadyrov, S.

In: Journal of Number Theory, Vol. 132, No. 11, 11.2012, p. 2499-2509.

Research output: Contribution to journalArticle

Gorodnik, A. ; Kadyrov, S. / Algebraic numbers, hyperbolicity, and density modulo one. In: Journal of Number Theory. 2012 ; Vol. 132, No. 11. pp. 2499-2509.
@article{06841acab1b34d82ae0260cb3f09c462,
title = "Algebraic numbers, hyperbolicity, and density modulo one",
abstract = "We prove the density of the sets of the form{λ 1 mμ 1 nξ 1+...+λ k mμ k nξk:m,n∈N} modulo one, where λ i and μ i are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelian groups.",
keywords = "Compact abelian group, Density modulo one, Higher-rank abelian action, Multiplicatively independent numbers",
author = "A. Gorodnik and S. Kadyrov",
year = "2012",
month = "11",
doi = "10.1016/j.jnt.2012.05.018",
language = "English",
volume = "132",
pages = "2499--2509",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press Inc.",
number = "11",

}

TY - JOUR

T1 - Algebraic numbers, hyperbolicity, and density modulo one

AU - Gorodnik, A.

AU - Kadyrov, S.

PY - 2012/11

Y1 - 2012/11

N2 - We prove the density of the sets of the form{λ 1 mμ 1 nξ 1+...+λ k mμ k nξk:m,n∈N} modulo one, where λ i and μ i are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelian groups.

AB - We prove the density of the sets of the form{λ 1 mμ 1 nξ 1+...+λ k mμ k nξk:m,n∈N} modulo one, where λ i and μ i are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelian groups.

KW - Compact abelian group

KW - Density modulo one

KW - Higher-rank abelian action

KW - Multiplicatively independent numbers

UR - http://www.scopus.com/inward/record.url?scp=84864389687&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864389687&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2012.05.018

DO - 10.1016/j.jnt.2012.05.018

M3 - Article

VL - 132

SP - 2499

EP - 2509

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 11

ER -