Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T02:37:15.180Z Has data issue: false hasContentIssue false

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: [email protected] Division of Pure Mathematics, Department of Mathematical Sciences, University of Liverpool, M&O Building, Liverpool, L69 3BX, United Kingdom, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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