《数域上傅里叶分析(英文版)》是一部学习数论和群论的研究生教程。每章的引入也是十分有意思，对历史材料的深入理解和作者对相关内容独到的理解和表达方式，使得本书组成一个有机的整体，这些正是一个初学者所需要的。同时，这本书也很适合于科研人员。书中包括了不少比较复杂的内容，使得这本书的部分内容比较难懂，也是本书吸引读者的一个原因。每章的后面都附有习题。本书由罗摩克里希纳著。

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