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

Faure, Henri

Acta Arith. 117, No. 2, 125-148 (2005).

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.

Reviewer: Robert F. Tichy (Graz)

MSC:

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

Keywords:

discrepancy; diaphony; generalized van der Corput sequences; digital \((0; 1)\)-sequences

Citations:

Zbl 1054.11039