Algebraic numbers, hyperbolicity, and density modulo one

作者：Gorodnik A^*; Kadyrov S

来源：Journal of Number Theory, 2012, 132(11): 2499-2509.

DOI：10.1016/j.jnt.2012.05.018

• Density modulo one
• Multiplicatively independent numbers
• Compact abelian group
• Higher-rank abelian action

We prove the density of the sets of the form %26lt;br%26gt;{lambda(m)(1)mu(n)(1)xi(1) + ... + lambda(m)(k)mu(n)(k)xi(k): m, n is an element of N} %26lt;br%26gt;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 abelian groups.

• 出版日期2012-11