Algebraic Numbers, Hyperbolicity, and Density Modulo One

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

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• Dynamics of large Group Actions, Rigidity and Diophantine Geometry

Gorodnik, A.

1/02/101/02/13

Project: Research