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Some effective results for ×a×b

Published online by Cambridge University Press:  21 May 2009

Institute for Advanced Study, Princeton, NJ 08540, USA
Princeton University, Princeton, NJ 08544, USA The Hebrew University, 91904 Jerusalem, Israel
EPFL, 1015 Lausanne, Switzerland Universit Montpellier, 34095 Montpellier, France
Stanford University, Stanford, CA 94305, USA Courant Institute of Mathematical Sciences, New York, NY 10012, USA
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We provide effective versions of theorems of Furstenberg and Rudolph–Johnson regarding closed subsets and probability measures of ℝ/ℤ invariant under the action of a non-lacunary multiplicative semigroup of integers. In particular, we give an explicit rate at which the sequence {anbkx}n,k becomes dense for a,b fixed multiplicatively independent integers and x∈ℝ/ℤ Diophantine generic.

Research Article
Copyright © Cambridge University Press 2009


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