Periodicity of \(p\)-adic continued fractions (Q913860)
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scientific article; zbMATH DE number 4148228
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Periodicity of \(p\)-adic continued fractions |
scientific article; zbMATH DE number 4148228 |
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Periodicity of \(p\)-adic continued fractions (English)
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1988
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\textit{Th. Schneider} [Symp. Math. 4, 181--189 (1970; Zbl 0222.10035)] defined continued fraction expansions for \(p\)-adic numbers. The author shows that contrary to the real case quadratic roots of rational integers lying in \(\mathbb Q_p\) may not have a periodic expansion. This happens in particular to all quadratic roots of negative numbers.
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quadratic irrationalities
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continued fraction expansions
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p-adic numbers
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periodic expansion
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