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罗摩克里希纳(DinakarRamakrishnan) 著
出版社: 世界图书出版公司 ISBN:9787510037511 版次:1 商品编码:10914299 包装:平装 外文名称:Fourier Analysis on Number Fields 开本:24开 出版时间:2011-07-01 页数:350 正文语种:英文
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
数域上的傅里叶分析 [Fourier Analysis on Number Fields] 电子书 下载 mobi epub pdf txt
数域上的傅里叶分析 [Fourier Analysis on Number Fields]-so88
数域上的傅里叶分析 [Fourier Analysis on Number Fields] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
罗摩克里希纳(DinakarRamakrishnan) 著
出版社: 世界图书出版公司 ISBN:9787510037511 版次:1 商品编码:10914299 包装:平装 外文名称:Fourier Analysis on Number Fields 开本:24开 出版时间:2011-07-01 页数:350 正文语种:英文
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
PREFACEINDEX 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
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