Duality in Analytic Number Theory (Cambridge Tracts in Mathematics): 122 (Cambridge Tracts in Mathematics, Series Number 122) - Softcover

Elliott, Peter D. T. A.

Softcover

ISBN 10: 0521058082 ISBN 13: 9780521058087

Publisher: Cambridge University Press, 2008

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.

About this title

Review:

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

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

Book Description:

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.

About this edition

• Publisher: Cambridge University Press
• Publication date: 2008
• ISBN 10: 0521058082
• ISBN 13: 9780521058087
• Binding: Paperback
• Number of pages: 360