Products and quotients of numbers with small partial quotients

Stephen Astels

Journal de théorie des nombres de Bordeaux (2002)

  • Volume: 14, Issue: 2, page 387-402
  • ISSN: 1246-7405

Abstract

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For any positive integer m let F ( m ) denote the set of numbers with all partial quotients (except possibly the first) not exceeding m . In this paper we characterize most products and quotients of sets of the form F ( m ) .

How to cite

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Astels, Stephen. "Products and quotients of numbers with small partial quotients." Journal de théorie des nombres de Bordeaux 14.2 (2002): 387-402. <http://eudml.org/doc/248891>.

@article{Astels2002,
abstract = {For any positive integer $m$ let $F(m)$ denote the set of numbers with all partial quotients (except possibly the first) not exceeding $m$. In this paper we characterize most products and quotients of sets of the form $F(m)$.},
author = {Astels, Stephen},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Cantor sets; number of small partial quotients},
language = {eng},
number = {2},
pages = {387-402},
publisher = {Université Bordeaux I},
title = {Products and quotients of numbers with small partial quotients},
url = {http://eudml.org/doc/248891},
volume = {14},
year = {2002},
}

TY - JOUR
AU - Astels, Stephen
TI - Products and quotients of numbers with small partial quotients
JO - Journal de théorie des nombres de Bordeaux
PY - 2002
PB - Université Bordeaux I
VL - 14
IS - 2
SP - 387
EP - 402
AB - For any positive integer $m$ let $F(m)$ denote the set of numbers with all partial quotients (except possibly the first) not exceeding $m$. In this paper we characterize most products and quotients of sets of the form $F(m)$.
LA - eng
KW - Cantor sets; number of small partial quotients
UR - http://eudml.org/doc/248891
ER -

References

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  1. [1] S. Astels, Cantor sets and numbers with restricted partial quotients (Ph.D. thesis). University of Waterloo, 1999. MR1491854
  2. [2] S. Astels, Cantor sets and numbers with restricted partial quotients. Trans. Amer. Math. Soc.352 (2000), 133-170. Zbl0967.11026MR1491854
  3. [3] S. Astels, Sums of numbers with small partial quotients. Proc. Amer. Math. Soc.130 (2001), 637-642. Zbl0992.11044MR1866013
  4. [4] S. Astels, Sums of numbers with small partial quotients II. J. Number Theory91 (2001), 187-205. Zbl1030.11002MR1876272
  5. [5] G.A. Freiman, Teorija cisel (Number Theory). Kalininskii Gosudarstvennyi Universitet, Moscow, 1973. MR429766
  6. [6] M. Hall, JR, On the sum and product of continued fractions. Ann. of Math.48 (1947), 966-993. Zbl0030.02201MR22568
  7. [7] G.H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers (Fourth Edition). Clarendon Press, Oxford, UK, 1960. Zbl0086.25803MR67125
  8. [8] H. Schecker, Uber die Menge der Zahlen, die als Minima quadratischer Formen auftreten. J. Number Theory9 (1977), 121-141. Zbl0351.10021MR466031

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