Title: Duality in Analytic Number Theory (Cambridge Tracts in Mathematics, Series Number 122)
Publisher: Cambridge University Press
Publication Date: 1997
Language: English
ISBN 10: 0521560888
ISBN 13: 9780521560887
Binding: Hardcover
Condition: New

About this title

Synopsis

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.

Book Description

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.

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