Cantor sets determined by partial quotients of continued fractions of Laurent series

Authors:
Xue-Hai Hu;Bao-Wei Wang;Jun Wu;Yue-Li Yu
Affiliations:
Department of Mathematics, Wuhan University, Wuhan, Hubei 430072, PR China;Department of Mathematics, Wuhan University, Wuhan, Hubei 430072, PR China;Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China;Department of Mathematics, Wuhan University, Wuhan, Hubei 430072, PR China
Venue:
Finite Fields and Their Applications
Year:
2008

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Abstract

In this paper, two types of general sets determined by partial quotients of continued fractions over the field of formal Laurent series with coefficients from a given finite field are studied. The Hausdorff dimensions of {x:degA"n(x)=@f(n),for infinitely many n} and {x:degA"n(x)=@f(n),@?n=1} are determined completely, where A"n(x) denotes the partial quotients in the continued fraction expansion (in case of Laurent series) of x and @f(n) is a positive valued function defined on natural numbers N.