Some metric properties of Lüroth expansions over the field of Laurent series (Q2758197)
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scientific article; zbMATH DE number 1679531
| Language | Label | Description | Also known as |
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| English | Some metric properties of Lüroth expansions over the field of Laurent series |
scientific article; zbMATH DE number 1679531 |
Statements
Some metric properties of Lüroth expansions over the field of Laurent series (English)
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1 December 2002
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Lüroth expansion
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Laurent series
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strong law of large numbers
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law of iterated logarithm
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central limit theorem
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\textit{J. Knopfmacher} and \textit{A. Knopfmacher} have produced various metric results on the coefficients of the Lüroth expansions of elements in the field of Laurent series in [Astérisque 15, 237-246 (1992; Zbl 0788.11031); see also \textit{J. Knopfmacher}, Acta Math. Hung. 60, 241-246 (1992; Zbl 0774.11073)]. In this paper the author generalizes these to similar subsequence results. The main theorem states that the coefficients of the Lüroth expansions are independent, identically distributed random variables. By applying various classical theorems from probability theory to this setting, several results are obtained.
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