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ON A PROBLEM OF ERDÖS AND MAHLER CONCERNING CONTINUED FRACTIONS

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  19 October 2016

JEAN LELIS  and
DIEGO MARQUES
JEAN LELIS
Affiliation:
Departamento de Matemática, Universidade de Brasília, Brasília, 70910-900, Brazil email jeancarlos@mat.unb.br
DIEGO MARQUES*
Affiliation:
Departamento de Matemática, Universidade de Brasília, Brasília, 70910-900, Brazil email diego@mat.unb.br
*
✉diego@mat.unb.br
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Abstract

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In 1939, Erdös and Mahler [‘Some arithmetical properties of the convergents of a continued fraction’, J. Lond. Math. Soc. (2)14 (1939), 12–18] studied some arithmetical properties of the convergents of a continued fraction. In particular, they raised a conjecture related to continued fractions and Liouville numbers. In this paper, we shall apply the theory of linear forms in logarithms to obtain a result in the direction of this problem.

Keywords

continued fractionsLiouville numberslinear forms in logarithms

MSC classification

Primary: 11J70: Continued fractions and generalizations
Secondary: 11J86: Linear forms in logarithms; Baker's method
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 2 , April 2017 , pp. 183 - 186
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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