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A generalization of Furstenberg's Diophantine Theorem

Authors:	Bryna Kra

Institution:	Department of Mathematics, University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, Michigan 49108-1109

Abstract:	We obtain a generalization of Furstenberg's Diophantine Theorem on non-lacunary multiplicative semigroups. For example we show that the sets of sums $\{(p_1^nq_1^m + p_2^nq_2^m)\alpha:n,m \in \mathbb{N}\}$ and $\{(p_1^nq_1^m + 2^n)\alpha: n,m \in \mathbb{N}\}$ are dense in the circle $\mathbb{T} = \mathbb{R}/ \mathbb{Z}$ for all irrational $\alpha$ , where are distinct pairs of multiplicatively independent integers for .

Keywords:	Topological dynamics distribution modulo $1$

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