Babu, Gutti Jogesh; Erdős, Paul A note on the distribution function of additive arithmetical functions in short intervals. (English) Zbl 0638.10049 Can. Math. Bull. 32, No. 4, 441-445 (1989). Let \(f\) be an additive arithmetic function having a distribution \(F\). For any sequence \(1\leq b(n)\leq n\), \(b(n)\to \infty\), let \[ Q_n(b,f)(x)=card\{n\leq m\leq n+b(n): f(m)\leq x\}/b(n). \] In this note, we determine the slowest growing function \(b\) so that \(Q_n(b,f)\) tends weakly to \(F\), for various \(f\). Reviewer: G.J.Babu Cited in 1 Document MSC: 11K65 Arithmetic functions in probabilistic number theory 60F05 Central limit and other weak theorems Keywords:short intervals; Erdős-Winter theorem; Erdős-Kac theorem; additive arithmetic function; distribution PDFBibTeX XMLCite \textit{G. J. Babu} and \textit{P. Erdős}, Can. Math. Bull. 32, No. 4, 441--445 (1988; Zbl 0638.10049) Full Text: DOI