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

 

Sums of numbers with small partial quotients


Author: S. Astels
Journal: Proc. Amer. Math. Soc. 130 (2002), 637-642
MSC (2000): Primary 11J70, 11Y65; Secondary 37C70
Published electronically: June 20, 2001
MathSciNet review: 1866013
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Abstract:

In a paper of James Hlavka it is stated that $F(3)+F(2)+F(2)\neq{\mathbb R}$. In this manuscript we show that this is false by establishing that $F(3)\pm F(2)\pm F(2)={\mathbb R}$. We also describe the corresponding products and quotients.


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Additional Information

S. Astels
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
Email: sastels@math.uga.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06136-6
PII: S 0002-9939(01)06136-6
Keywords: Continued fractions, Cantor sets, sums of sets
Received by editor(s): August 28, 2000
Published electronically: June 20, 2001
Additional Notes: The author’s research was supported in part by the Natural Sciences and Engineering Research Council of Canada.
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2001 American Mathematical Society