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Duality in Analytic Number Theory By Peter D. T. A. Elliott


作者: Analytic Number Theory, By Peter, T. A. Elliott

日期: 01.01.2011

ISBN: 0521560888

页数: 360

出版社: //C]U,P 1997

标签: 数学



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Duality in Analytic Number Theory By Peter D T A Elliott


Duality in Analytic Number Theory By Peter D. T. A. Elliott

PUBLISHER: //C]U,P 1997 | 360 PAGES | ISBN: 0521560888 , 0521058082 | PDF |12.23 MB



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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