Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Elementary proof of Furstenberg's Diophantine result


Author: Michael D. Boshernitzan
Journal: Proc. Amer. Math. Soc. 122 (1994), 67-70
MSC: Primary 11K31
DOI: https://doi.org/10.1090/S0002-9939-1994-1195714-X
MathSciNet review: 1195714
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present an elementary proof of a diophantine result (due to H. Furstenberg) which asserts (in a special case) that for every irrational $ \alpha $ the set $ \{ {2^m}{3^n}\alpha \vert m,n \geq 0\} $ is dense modulo 1. Furstenberg's original proof employs the theory of disjointness of topological dynamical systems.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11K31

Retrieve articles in all journals with MSC: 11K31


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1195714-X
Keywords: Distribution modulo 1, topological dynamics
Article copyright: © Copyright 1994 American Mathematical Society