内容简介
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 harmonic analysis on
topological groups. The more particular goal is to cover John
Tate’s 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 Tate’s thesis are somewhat terse and&nbs..
目录
PREFACE
INDEX OF NOTATION
1 TOPOLOGICAL GROUPS
1.1 Basic Notions
1.2 Haar Measure
1.3 Profinite Groups
1.4 Pro-p-Groups
Exercises
2 SOME REPRESENTATION THEORY
2.1 Representations of Locally Compact Groups
2.2 Banach Algebras and the Gelfand Transform
2.3 The Spectral Theorems
2.4 Unitary Representations
Exercises
3 DUALITY FOR LOCALLY COMPACT ABELIAN GROUPS
3.1 The Pontryagin Dual
3.2 Functions of Positive Type
3.3 The Fourer Inversion Formula
3.4 Pontryagin Duality
Exercises
4 THE STRUCTURE OF ARITHMETIC FIELDS
5 ADELES, IDELES, AND THE CLASS GROUPS
6 A QUICK TOUR OF CLASS FIELD THEO..
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