Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: July 15, 2002
MathSciNet review: 1918819
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $\{ n\alpha \},\;n\in \mathcal N$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11K06, 11B05

Retrieve articles in all journals with MSC (2000): 11K06, 11B05


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: http://dx.doi.org/10.1090/S0002-9939-02-06791-6
PII: S 0002-9939(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