Fourier Analysis on Number Fields 

Author:
 Ramakrishnan, Dinakar Valenza, Robert J. 
Series title:  Graduate Texts in Mathematics Ser. 
ISBN:  9781475730876 
Publication Date:  Mar 2013 
Publisher:  Springer

Book Format:  Paperback 
List Price:  USD $99.00 
Book Description:

A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries  technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and...
More DescriptionA modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries  technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduatelevel course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.