Approximation orders of formal Laurent series by β-expansions |
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Authors: | Shuai Ling Wang |
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Institution: | aSchool of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, PR China |
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Abstract: | We prove that almost all (with respect to Haar measure) formal Laurent series are approximated with the linear order −(degβ)n by their β-expansions convergents. Hausdorff dimensions of sets of Laurent series which are approximated by all other orders, are determined. In contrast, the corresponding theory of real case has not been established. |
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Keywords: | β -Expansion Approximation Laurent series Finite field Hausdorff dimension |
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