Duality in Analytic Number Theory (Cambridge Tracts in Mathematics) - Brossura

Elliott, Peter D. T. A.

Brossura

ISBN 10: 0521058082 ISBN 13: 9780521058087

Casa editrice: Cambridge University Press, 2008

Riassunto

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.

Su questo libro

Recensione:

' ... a fruitful atempt in finding a general method in Analytic Number Theory.' Monatshefte für Mathematik

' ... quite remarkable publication.' European Mathematical Society

Descrizione del libro:

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 construct their proofs.

Su questa edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 2008
• ISBN 10: 0521058082
• ISBN 13: 9780521058087
• Rilegatura: Copertina flessibile
• Numero di pagine: 360