Gorodnik A.Kadyrov S.2025-08-042025-08-042012Gorodnik A , Kadyrov S / Algebraic numbers, hyperbolicity, and density modulo one / Journal of Number Theory / 20122499-2509https://repository.sdu.edu.kz/handle/123456789/1846We 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.enDensity modulo oneMultiplicatively independent numbersHigher-rank abelian actionArticle