Algebraic numbers, hyperbolicity, and density modulo one

A. Gorodnik, S. Kadyrov

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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 1 2012

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Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

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