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 languageEnglish
Pages (from-to)2499-2509
Number of pages11
JournalJournal of Number Theory
Volume132
Issue number11
DOIs
Publication statusPublished - Nov 2012
Externally publishedYes

Fingerprint

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.
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