Arithmetical Functions

Characterizes certain multiplicative and additive arithmetical functions by combining methods from number theory with simple ideas from functional and harmonic analysis.

Wolfgang Schwarz (Author), Jürgen Spilker (Author)

9780521427258, Cambridge University Press

Paperback, published 10 March 1994

388 pages
22.8 x 15.2 x 2.1 cm, 0.55 kg

"...a pleasant, courteous, thorough introduction to some of the more civilized areas of number theory, especially spaces of arithmetical functions and allied subjects...downright readable, and a book to be owned by every library, without question." The Bulletin of Mathematics Books

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.

Preface
Acknowledgements
Notation
1. Tools from number theory
Photographs
2. Mean-value theorems and multiplicative functions, I
3. Related arithmetical functions
4. Uniformly almost-periodic arithmetical functions
5. Ramanujan Expansions of functions in Bu
6. Almost-periodic and almost-even arithmetical functions
Photographs
7. The theorems of Elliott and Daboussi
8. Ramanujan expansions
9. Mean-value theorems and multiplicative functions, II
Photographs
Appendix
Bibliography
Author index
Subject index
Photographs
Acknowledgements.

Subject Areas: Number theory [PBH]