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OverviewThe 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. Full Product DetailsAuthor: Wolfgang Schwarz (Johann Wolfgang Goethe-Universität Frankfurt) , Jürgen Spilker (Albert-Ludwigs-Universität Freiburg, Germany)Publisher: Cambridge University Press Imprint: Cambridge University Press Volume: 184 ISBN: 9781107359963ISBN 10: 1107359961 Publication Date: 05 June 2013 Audience: Professional and scholarly , Professional & Vocational Format: Undefined Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsPreface; 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.Reviews...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 ...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 Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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