## 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

Zbl 1054.11039
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