Arithmetical functions : An introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties

Includes index

Includes bibliography (p. 333-352) and references.

1. Simple tools from number theory
2. Mean-value theorems and multiplicative functions
3. Related multiplicative functions
4. Spaces of uniformly almost periodic arithmetic functions

The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mean-value theorems, and properties of related multiplicative functions. They also prove the mean-value theorems of Wirsing and Halász and study the pointwise convergence of the Ramanujan expansion. Finally, some applications to power series with multiplicative coefficients are included, along with exercises and an extensive bibliography.