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On the sum of degrees of digits occurring in continued fraction expansions of Laurent series

Published online by Cambridge University Press:  03 February 2005

JUN WU
JUN WU
Affiliation:
Department of Mathematics, Wuhan University, Wuhan 430072, China. e-mail: wujunyu@public.wh.hb.cn
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Abstract

Bescovitch considered the Hausdorff dimensions of sets related to the sum of digits of real numbers represented in the dyadic expansions. In this paper, we provide an analogy for continued fraction expansions over the field of formal Laurent series. We also calculate the Hausdorff dimensions of sets of Laurent series which have given polynomial or exponential approximation orders. Such approximations converge faster than those of almost all Laurent series (with respect to the Haar measure).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 138 , Issue 1 , January 2005 , pp. 9 - 20
Copyright
2005 Cambridge Philosophical Society

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