Duality in Analytic Number Theory

Peter D. Elliott

ISBN 10: 0521560888 / ISBN 13: 9780521560887

Edité par Cambridge University Press, 1997

A propos de cet article

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.

N° de réf. du vendeur 9780521560887

Détails bibliographiques

• Titre: Duality in Analytic Number Theory
• Éditeur: Cambridge University Press
• Date de parution: 1997
• Langue: anglais
• ISBN à 10 chiffres: 0521560888
• ISBN à 13 chiffres: 9780521560887
• Reliure: Buch
• État de l'article: Neu

A propos de ce titre

Synopsis

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 application, the book also illustrates a way of thinking mathematically: historical background is 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 arithmetical 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 individual topics.