Fourier Analysis On Number Fields - Ramakrishnan; Valenza

Descripción

LIBRERÍA LEA+

The general aim of this book is to provide a modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasizing harmonica analysis on topological groups. The more particular goal is to cover John Tate´s visionaty thesis, giving virtually all of the necessary analytic details and topological preliminaries-technical prerequisites that are often foreign o the typical, more algebraically inclined numer theorist. While most of the existing treatments of Tate´s thesis are somewhat terse and less than complete, the authors´ intent is to be more leisurely, more comprehensive, and more comprehensive. The text addresses sudents who have taken a year of graduate-level courses in algebra, analysis, and topology. 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 theoristis, but also to students of harmonic analysis or the representation theory of Lie groups. Moreover, the work should be a good reference for working mathematicians interested in anay of these fields. Specific topics include: topological groups, representation theory, duality for locally compact abelian groups, the structure of arithmetic fields, adeles and ideles, an introduction to class field theory, and Tate´s thesis and applications.

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