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内容简介

This book grew out of notes from several courses that the first author has taught over the past nine years at the California Institute of Technology, and earlier at the Johns Hopkins University, Cornell University, the University of Chicago,and the University of Crete. Our general aim is to provide a modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasizing harmonic analysis on topological groups. Our more particular goal is to cover John Tate's visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries——technical prereq-uisites that are often foreign to the typical, more algebraically inclined number theorist. Most of the existing treatments of Tate's thesis, including Tate's own,range from terse to cryptic; our intent is to be more leisurely, more comprehen-sive, and more comprehensible. To this end we have assembled material that has admittedly been treated elsewhere, but not in a single volume with so much detail and not with our particular focus.

内页插图

目录

PREFACE
INDEX OF NOTATION
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 Fourier Inversion Formula
3.4 Pontryagin Duality
Exercises

4 THE STRUCTURE OF ARITHMETIC FIELDS
4. I The Module of an Automorphism
4.2 The Classification of Locally Compact Fields
4.3 Extensions of Local Fields
4.4 Places and Completions of Global Fields
4.5 Ramification and Bases
Exercises

5 ADELES, IDELES, AND THE CLASS GROUPS
5.1 Restricted Direct Products, Characters, and Measures
5.2 Adeles, Ideles, and the Approximation Theorem
5.3 The Geometry of Ar/K
5.4 The Class Groups
Exercises

6 A QUICK TOUR OF CLASS FIELD THEORY
6.1 Frobenius Elements
6.2 The Tchebotarev Density Theorem
6.3 The Transfer Map
6.4 Artin's Reciprocity Law
6.5 Abelian Extensions of Q and Qp
Exercises

7 TATE'S THESIS AND APPLICATIONS
7.1 Local （-Functions
7.2 The Riemann-Roch Theorem
7.3 The Global Functional Equation
7.4 Hecke L-Functions .
7.5 The Volume of C and the Regulator
7.6 Dirichlet's Class Number Formula
7.7 Nonvanishing on the Line Re（s）——I
7.8 Comparison of Hecke L-Functions
Exercises

APPENDICES
Appendix A: Normed Linear Spaces
A. 1 Finite-Dimensional Normed Linear Spaces
A.2 The Weak Topology
A.3 The Weak-Slat Topology
A.4 A Review of LP-Spaces and Duality
Appendix B: Dedekind Domains
B.1 Basic Properties
B.2 Extensions of Dedekind Domains
REFERENCES
INDEX

前言/序言

数域上的傅里叶分析 [Fourier Analysis on Number Fields] 电子书 下载 mobi epub pdf txt

评分☆☆☆☆☆

GTM的书太适合裁对基础数学热爱的人了

评分☆☆☆☆☆

有帮助

评分☆☆☆☆☆

包装还行，活动时买的。还没看，先收藏。

评分☆☆☆☆☆

这本书非常的不错，值得阅读。它从一般意义上的傅里叶分析推广到了一般数域上，使得我们在一般的数域上可以对其进行分析的运算，这其中也用到了拓扑，测度论等知识，如果大家想真正地读懂这本书的细节，最好还是要去看看拓扑，代数，测度和表示的基本知识，希望大家能够从这本书中，真正地了解代数上的分析学问。祝大家阅读愉快！

评分☆☆☆☆☆

这本书非常的不错，值得阅读。它从一般意义上的傅里叶分析推广到了一般数域上，使得我们在一般的数域上可以对其进行分析的运算，这其中也用到了拓扑，测度论等知识，如果大家想真正地读懂这本书的细节，最好还是要去看看拓扑，代数，测度和表示的基本知识，希望大家能够从这本书中，真正地了解代数上的分析学问。祝大家阅读愉快！

评分☆☆☆☆☆

这本书非常的不错，值得阅读。它从一般意义上的傅里叶分析推广到了一般数域上，使得我们在一般的数域上可以对其进行分析的运算，这其中也用到了拓扑，测度论等知识，如果大家想真正地读懂这本书的细节，最好还是要去看看拓扑，代数，测度和表示的基本知识，希望大家能够从这本书中，真正地了解代数上的分析学问。祝大家阅读愉快！

评分☆☆☆☆☆

全英文的书，很有味道，角度不一样

评分☆☆☆☆☆

一本相当不错的数学书，推荐！

评分☆☆☆☆☆

口水很久了

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