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 Halasz 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.
Rezensionen / Stimmen
"...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
Reihe
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
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Worked examples or Exercises
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 23 mm
Gewicht
ISBN-13
978-0-521-42725-8 (9780521427258)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Johann Wolfgang Goethe-Universitaet Frankfurt
Albert-Ludwigs-Universitaet Freiburg, Germany
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.
