Algebraic Numbers, Hyperbolicity, and Density Modulo One

A Gorodnik; S Kadyrov

doi:10.1016/j.jnt.2012.05.018

Algebraic Numbers, Hyperbolicity, and Density Modulo One

A Gorodnik, S Kadyrov

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

Abstract

We prove the density of the sets of the form ${{\lambda}_1^m {\mu}_1^n {\xi}_1 +...+{\lambda}_k^m {\mu}_k^n {\xi}_k : m,n \in \mathbb N}$ modulo one, where $\lambda_i$ and $\mu_i$ are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelean groups.

Translated title of the contribution	Algebraic Numbers, Hyperbolicity, and Density Modulo One
Original language	English
Number of pages	12
Journal	Journal of Number Theory
DOIs	https://doi.org/10.1016/j.jnt.2012.05.018
Publication status	Published - 2012

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10.1016/j.jnt.2012.05.018

http://arxiv.org/abs/1109.0183

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Dynamics of large Group Actions, Rigidity and Diophantine Geometry
Gorodnik, A.
1/02/10 → 1/02/13
Project: Research

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@article{447b7f162f4d4d1cab9f7ddd6ba7bf20,

title = "Algebraic Numbers, Hyperbolicity, and Density Modulo One",

abstract = "We prove the density of the sets of the form ${{\lambda}_1^m {\mu}_1^n {\xi}_1 +...+{\lambda}_k^m {\mu}_k^n {\xi}_k : m,n \in \mathbb N}$ modulo one, where $\lambda_i$ and $\mu_i$ are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelean groups.",

author = "A Gorodnik and S Kadyrov",

year = "2012",

doi = "10.1016/j.jnt.2012.05.018",

language = "English",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press",

}

TY - JOUR

T1 - Algebraic Numbers, Hyperbolicity, and Density Modulo One

AU - Gorodnik, A

AU - Kadyrov, S

PY - 2012

Y1 - 2012

N2 - We prove the density of the sets of the form ${{\lambda}_1^m {\mu}_1^n {\xi}_1 +...+{\lambda}_k^m {\mu}_k^n {\xi}_k : m,n \in \mathbb N}$ modulo one, where $\lambda_i$ and $\mu_i$ are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelean groups.

AB - We prove the density of the sets of the form ${{\lambda}_1^m {\mu}_1^n {\xi}_1 +...+{\lambda}_k^m {\mu}_k^n {\xi}_k : m,n \in \mathbb N}$ modulo one, where $\lambda_i$ and $\mu_i$ are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelean groups.

U2 - 10.1016/j.jnt.2012.05.018

DO - 10.1016/j.jnt.2012.05.018

M3 - Article (Academic Journal)

SN - 0022-314X

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Algebraic Numbers, Hyperbolicity, and Density Modulo One

Abstract

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Dynamics of large Group Actions, Rigidity and Diophantine Geometry

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