Algebraic Numbers, Hyperbolicity, and Density Modulo One

A Gorodnik, S Kadyrov

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 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 contributionAlgebraic Numbers, Hyperbolicity, and Density Modulo One
Original languageEnglish
Number of pages12
JournalJournal of Number Theory
DOIs
Publication statusPublished - 2012

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