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Distinct gaps between fractional parts of sequences

Author(s): Marian Vâjâitu; Alexandru Zaharescu
Journal: Proc. Amer. Math. Soc. 130 (2002), 3447-3452.
MSC (2000): Primary 11K06, 11B05
Posted: July 15, 2002
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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: 10.1090/S0002-9939-02-06791-6
PII: S 0002-9939(02)06791-6
Received by editor(s): February 7, 2001
Posted: July 15, 2002
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2002, American Mathematical Society

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