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Some metric properties of Lüroth expansions over the field of Laurent series

Published online by Cambridge University Press:  17 April 2009

Simon Kristensen
Affiliation:
Institut de Recherche Mathematique Avancée de Strasbourg, 7, rue René Descartes, 67084 Strasbourg, France, e-mail: kristens@math.u-strasbg.fr Division of Pure Mathematics, Department of Mathematical Sciences, University of Liverpool, M&O Building, Liverpool, L69 3BX, United Kingdom, e-mail: simonkr@liverpool.ac.uk
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J. Knopfmacher and A. Knopfmacher have previously produced some metric results concerning the coefficients of the Lüroth expansions of elements in the field of Laurent series with coefficients from a finite field. In this paper, we obtain analogous metric results for subsequences of the coefficients of the expansions.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Breiman, L., Probability. (Corrected reprint of the 1968 original), Classics in Applied Mathematics (Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992).CrossRefGoogle Scholar
[2]Jager, H. and de Vroedt, C., ‘Lüroth series and their ergodic properties’, Nederl. Akad. Wetensch. Proc. Ser. A 72 = Indag. Math. 31 (1969), 3142.CrossRefGoogle Scholar
[3]Jones, W.B. and Thron, W.J., Continued fractions. (With a foreword by Felix E. Browder, With an introduction by Peter Henrici), Encyclopedia of Mathematics and its Applications 11 (Addison-Wesley Publishing Co., Reading, MA, 1980).Google Scholar
[4]Knopfmacher, J., ‘Ergodic properties of some inverse polynomial series expansions of Laurent series’, Acta Math. Hungar. 60 (1992), 241246.CrossRefGoogle Scholar
[5]Knopfmacher, J. and Knopfmacher, A., ‘Metric properties of algorithms inducing Lüroth series expansions of Laurent series’, Astérisque 15 (1992), 237246.Google Scholar
[6]Sprindžuk, V.G., Mahler's problem in metric number theroy. (Translated from the Russian by Volkmann, B.), Translations of Mathematical Monographs 25 (American Mathematical Society, Providence, R. I., 1969).Google Scholar