Introduction to arithmetical functions. (English) Zbl 0591.10003

McCarthy, Paul J.

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

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