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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniform distribution modulo one
on subsequences


Author: Chris Hill
Journal: Proc. Amer. Math. Soc. 127 (1999), 1981-1986
MSC (1991): Primary 11K06; Secondary 11B05
Published electronically: March 17, 1999
MathSciNet review: 1605964
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $\mathcal{P}$ be a set of primes with a divergent series of reciprocals and let $\mathcal{K} = \mathcal{K}(\mathcal{P} )$ denote the set of squarefree integers greater than one that are divisible only by primes in $\mathcal{P}$. G. Myerson and A. D. Pollington proved that $(u_{n})_{n\geq 1}\subset [0,1)$ is uniformly distributed (mod 1) whenever the subsequence $(u_{kn})_{n\geq 1}$ is uniformly distributed (mod 1) for every $k$ in $\mathcal{K}$. We show that in fact $(u_{n})_{n\geq 1}$ is uniformly distributed (mod 1) whenever the subsequence $(u_{pn})_{n\geq 1}$ is uniformly distributed (mod 1) for every $p\in \mathcal{P}$.


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Additional Information

Chris Hill
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Address at time of publication: Department of Mathematics and Computer Science, Grinnell College, Grinnell, Iowa 50112
Email: hillc@math.grin.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04877-7
PII: S 0002-9939(99)04877-7
Received by editor(s): October 21, 1997
Published electronically: March 17, 1999
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society