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Discrepancy and diaphony of digital \((0,1)\)-sequences in prime base. (English) Zbl 1080.11054

This article is devoted to a precise study of the extreme discrepancy, the \(L^{2}\)-discrepancy and the diaphony of a class of digital \((0,1)\)-sequences in prime bases. The author derives explicit formulas for these quantities. The proofs depend on recent work of G. Larcher and F. Pillichshammer [Acta Arith. 106, 379–408 (2003; Zbl 1054.11039)] concerning the application of Walsh series analysis in base \(2\) to the analysis of discrepancy problems of digital sequences.

MSC:

11K38 Irregularities of distribution, discrepancy
11K06 General theory of distribution modulo \(1\)
11K31 Special sequences

Citations:

Zbl 1054.11039
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