McCarthy, Paul J. Introduction to arithmetical functions. (English) Zbl 0591.10003 Universitext. New York etc.: Springer-Verlag, VII, 365 p. DM 98.00 (1986). The author gives a well-written introduction into the elementary theory of arithmetical functions. All important topics of the subject are touched either in the main text or in the exercises (more than 400 and very well selected). We find here a.o. the theory of Ramanujan sums, generating functions and applications to the counting of congruence solutions as well as various generalizations of Dirichlet’s convolutions. There is also a chapter on asymptotic properties, but unfortunately it provides only few results based mostly on summation inversion. Each chapter ends with useful bibliographical and historical comments. The book is easy to read and does not presuppose from the reader more than a first course in number theory. Reviewer: W.Narkiewicz Cited in 9 ReviewsCited in 74 Documents MSC: 11A25 Arithmetic functions; related numbers; inversion formulas 11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory 11A07 Congruences; primitive roots; residue systems 11N37 Asymptotic results on arithmetic functions Keywords:arithmetic functions; arithmetic convolutions; Ramanujan sums PDF BibTeX XML Online Encyclopedia of Integer Sequences: d_3(n), or tau_3(n), the number of ordered factorizations of n as n = r s t.