Duality in analytic number theory
In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its applications, the boo...
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
1997
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| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
122 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| Zusammenfassung: | In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its applications, the book also illustrates a way of thinking mathematically: historical background in woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetic analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach Connections with other branches of analysis are illustrated by over 250 exercises, structured in chains about individuals topics |
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| Beschreibung: | XVIII, 341 S. |
| ISBN: | 0521560888 |