Rosochowicz, E. On weak uniform distribution of sequences of integers. (English) Zbl 0695.10038 Colloq. Math. 57, No. 1, 173-182 (1989). A characterization is given of subsets \(A\) of positive integers with the property that there exists a sequence weakly uniformly distributed (mod \(N\)) if and only if \(N\) belongs to \(A\). This solves Problem I in the reviewer’s “Uniform distribution of sequences of integers in residue classes” [Lect. Notes Math. 1087. Berlin: Springer (1984; Zbl 0541.10001), p. 9]. The author utilizes a method used by A. Zame [Colloq. Math. 24, 271–273 (1972; Zbl 0244.10048)] to solve a similar problem concerning uniform distribution. The same result has been obtained independently by another method by I. Z. Ruzsa [Colloq. Math. 57, 183–187 (1989; Zbl 0695.10039)]. Reviewer: Władysław Narkiewicz (Wrocław) Cited in 1 Review MSC: 11K65 Arithmetic functions in probabilistic number theory 11B50 Sequences (mod \(m\)) 11N64 Other results on the distribution of values or the characterization of arithmetic functions Keywords:weak uniform distribution; distribution of sequences of integers in residue classes Citations:Zbl 0695.10039; Zbl 0541.10001; Zbl 0244.10048 PDFBibTeX XMLCite \textit{E. Rosochowicz}, Colloq. Math. 57, No. 1, 173--182 (1989; Zbl 0695.10038) Full Text: DOI