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Distinct gaps between fractional parts of sequences


Authors: Marian Vâjâitu and Alexandru Zaharescu
Journal: Proc. Amer. Math. Soc. 130 (2002), 3447-3452
MSC (2000): Primary 11K06, 11B05
DOI: https://doi.org/10.1090/S0002-9939-02-06791-6
Published electronically: July 15, 2002
MathSciNet review: 1918819
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Abstract: Let $\alpha$ be a real number, $N$ a positive integer and $\mathcal N$a subset of $\{0,1,2,\dots,N\}$. We give an upper bound for the number of distinct lengths of gaps between the fractional parts $\{ n\alpha \},\;n\in \mathcal N$.


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Additional Information

Marian Vâjâitu
Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, Romania
Email: mvajaitu@stoilow.imar.ro

Alexandru Zaharescu
Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, Romania – and – Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, Illinois 61801
Email: zaharesc@math.uiuc.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06791-6
Received by editor(s): February 7, 2001
Published electronically: July 15, 2002
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2002 American Mathematical Society

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