Algebraic numbers, hyperbolicity, and density modulo one
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Date
2012
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Journal of Number Theory
Abstract
We prove the density of the sets of the form λm 1 μn 1ξ1 +···+ λm k μn k ξk: m,n ∈ N modulo one, where λi and μi are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelian groups.
Description
Keywords
Density modulo one, Multiplicatively independent numbers, Higher-rank abelian action
Citation
Gorodnik A , Kadyrov S / Algebraic numbers, hyperbolicity, and density modulo one / Journal of Number Theory / 2012