Arithmetical Functions [Paperback]

Characterizes certain multiplicative and additive arithmetical functions by combining methods from number theory with simple ideas from functional and harmonic analysis.The theme of this book is the characterization of certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. Applications to power series with multiplicative coefficients are also included.The theme of this book is the characterization of certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. Applications to power series with multiplicative coefficients are also included.The theme of this book is the characterization of 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. ...a pleasant, courteous, thorl)