Continuous nowhere differentiable functions and algebraic integers (Q1890794)
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scientific article; zbMATH DE number 757776
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Continuous nowhere differentiable functions and algebraic integers |
scientific article; zbMATH DE number 757776 |
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Continuous nowhere differentiable functions and algebraic integers (English)
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17 April 1996
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If \(\varepsilon_n(x)\) represents the coefficient of \(\beta^{- n}\) in the expansion of \(x\) in base \(\beta\), we consider the function defined as the sum of the series whose \(n\)th term is \(\varepsilon_n(x) \alpha^{- n}\). The paper shows that if \(\alpha\) and \(\beta\) are conjugate algebraic integers satisfying certain conditions then the function so defined is continuous but nowhere differentiable.
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continuous nowhere differentiable function
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