数域上的傅里叶分析(英文版)

本书是一部学习数论和 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。

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 Fourier Inversion Formula 3.4 Pontryagin Duality Exercises 4 THE STRUCTURE OF ARITHMETIC FIELDS 4.1 The Module Of an Automorphism 4.2 The Classification ofLocally 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 Ak/K 5.4 The Class Groups Exercises 6 A QUICK TOUR 0F CLASS FIELD THEORY 6.1 Frobenius Eiements 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 tile Line Re(s)=1 7.8 Comparison of Hecke L-Functions Exercises