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 be a set of primes with a divergent series of reciprocals and let denote the set of squarefree integers greater than one that are divisible only by primes in . G. Myerson and A. D. Pollington proved that is uniformly distributed (mod 1) whenever the subsequence is uniformly distributed (mod 1) for every in . We show that in fact is uniformly distributed (mod 1) whenever the subsequence is uniformly distributed (mod 1) for every .

**1.**P. D. T. A. Elliott,*Probabilistic number theory. I*, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 239, Springer-Verlag, New York-Berlin, 1979. Mean-value theorems. MR**551361****2.**Richard R. Hall,*Sets of multiples*, Cambridge Tracts in Mathematics, vol. 118, Cambridge University Press, Cambridge, 1996. MR**1414678****3.**L. Kuipers and H. Niederreiter,*Uniform distribution of sequences*, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. MR**0419394****4.**G. Myerson and A. D. Pollington,*Notes on uniform distribution modulo one*, J. Austral. Math. Soc. Ser. A**49**(1990), no. 2, 264–272. MR**1061047**

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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

Received by editor(s):
October 21, 1997

Published electronically:
March 17, 1999

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 1999
American Mathematical Society