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In this stimulating book, 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 application, the book also illustrates a way of thinking mathematically: The author weaves historical background into the narrative, while variant proofs illustrate obstructions, false steps and the development of insight in a manner reminiscent of Euler. He demonstrates 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 arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions previously beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, topically arranged.
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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. Besides its application, the book also illustrates a way of thinking mathematically: the author weaves historical background into the narrative, variant proofs illustrate obstructions, false steps and the development of insight. It is shown how to formulate theorems as well as how to construct their proofs. Connections with other branches of analysis are illustrated by over 250 exercises, structured in chains about individual topics.
Review:
"The subject area of the book is one which is studied by relatively few specialists. However, given the widespread occurence of these ideas, this volume deserves a place in any library used by analytic number theorists." D.R. Heath-Brown
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- PublisherCambridge University Press
- Publication date1997
- ISBN 10 0521560888
- ISBN 13 9780521560887
- BindingHardcover
- Edition number1
- Number of pages360
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Duality in Analytic Number Theory (Cambridge Tracts in Mathematics, Series Number 122)
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Book Description Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In this stimulating book, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory. He also illustrates a way of thinking mathematically and shows how to formulate theorems as well as cons. Seller Inventory # 446940046
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Book Description Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - In this stimulating book, 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 application, the book also illustrates a way of thinking mathematically: The author weaves historical background into the narrative, while variant proofs illustrate obstructions, false steps and the development of insight in a manner reminiscent of Euler. He demonstrates 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 arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions previously beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, topically arranged. Seller Inventory # 9780521560887
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