On the theory of \(b\)-adic diaphony (Q2720947)
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scientific article; zbMATH DE number 1611747
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the theory of \(b\)-adic diaphony |
scientific article; zbMATH DE number 1611747 |
Statements
1 July 2001
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\(b\)-adic diaphony
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irregularities of distributions
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On the theory of \(b\)-adic diaphony (English)
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A dyadic version of diaphony was defined [\textit{P. Hellekalek} and \textit{H. Leeb} [Acta Arith. 80, No. 2, 187--196 (1997; Zbl 0868.11034)] by using Walsh functions. Here a \(b\)-adic version of the diaphony in terms of the Chrestenson-Levy generalization of the Walsh functions is introduced. The authors show that the \(b\)-adic diaphony is a numerical quantity of irregularities of distributions. An order \(O(N^{-1} \sqrt{\log N})\) of the \(b\)-adic diaphony is obtained.
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