Products and quotients of numbers with small partial quotients
Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 387-402

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).

On note F(m) l’ensemble des nombres dont tous les quotients partiels (autres que le premier) sont inférieurs à m. Dans cet article, nous nous intéressons aux produits et quotients d’ensembles du type F(m).

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     author = {Stephen Astels},
     title = {Products and quotients of numbers with small partial quotients},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {387--402},
     year = {2002},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
     number = {2},
     doi = {10.5802/jtnb.364},
     zbl = {1074.11034},
     mrnumber = {2040683},
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     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.364/}
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Stephen Astels. Products and quotients of numbers with small partial quotients. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 387-402. doi: 10.5802/jtnb.364

[1] S. Astels, Cantor sets and numbers with restricted partial quotients (Ph.D. thesis). University of Waterloo, 1999. | MR | Zbl

[2] S. Astels, Cantor sets and numbers with restricted partial quotients. Trans. Amer. Math. Soc. 352 (2000), 133-170. | MR | Zbl

[3] S. Astels, Sums of numbers with small partial quotients. Proc. Amer. Math. Soc. 130 (2001), 637-642. | MR | Zbl

[4] S. Astels, Sums of numbers with small partial quotients II. J. Number Theory 91 (2001), 187-205. | MR | Zbl

[5] G.A. Freiman, Teorija cisel (Number Theory). Kalininskii Gosudarstvennyi Universitet, Moscow, 1973. | MR | Zbl

[6] M. Hall, JR, On the sum and product of continued fractions. Ann. of Math. 48 (1947), 966-993. | MR | Zbl

[7] G.H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers (Fourth Edition). Clarendon Press, Oxford, UK, 1960. | MR | Zbl

[8] H. Schecker, Uber die Menge der Zahlen, die als Minima quadratischer Formen auftreten. J. Number Theory 9 (1977), 121-141. | MR | Zbl

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