Algebraic Numbers, Hyperbolicity, and Density Modulo One

Alexander Gorodnik; Shirali Kadyrov

Algebraic Numbers, Hyperbolicity, and Density Modulo One

Dynamical Systems 2011-09-02 v1 Number Theory

Authors: Alexander Gorodnik , Shirali Kadyrov

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.

Keywords

additive number theory modular forms highest weight modules

Cite

@article{arxiv.1109.0183,
  title  = {Algebraic Numbers, Hyperbolicity, and Density Modulo One},
  author = {Alexander Gorodnik and Shirali Kadyrov},
  journal= {arXiv preprint arXiv:1109.0183},
  year   = {2011}
}

Algebraic Numbers, Hyperbolicity, and Density Modulo One

Abstract

Keywords

Cite

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