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arXiv · 1109.0183

Algebraic Numbers, Hyperbolicity, and Density Modulo One

Alexander Gorodnik·Shirali Kadyrov
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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.

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Alexander Gorodnik, Shirali Kadyrov. 2011-09-01. Algebraic Numbers, Hyperbolicity, and Density Modulo One. https://arxiv.org/abs/1109.0183

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