數域上的傅裏葉分析 [Fourier Analysis on Number Fields] pdf epub mobi txt 電子書 下載 2025

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☆☆☆☆☆

羅摩剋裏希納（DinakarRamakrishnan） 著

齣版社： 世界圖書齣版公司

ISBN：9787510037511

版次：1

商品編碼：10914299

包裝：平裝

外文名稱：Fourier Analysis on Number Fields

開本：24開

齣版時間：2011-07-01

頁數：350

正文語種：英文

內容簡介

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.

內頁插圖

目錄

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

評分☆☆☆☆☆

有幫助

評分☆☆☆☆☆

有幫助

評分☆☆☆☆☆

GTM的書太適閤裁對基礎數學熱愛的人瞭

評分☆☆☆☆☆

數學加英語，一舉兩得

評分☆☆☆☆☆

有幫助

評分☆☆☆☆☆

這是一本數論書，有一定的難度。傅立葉分析幾百年來一直是數學的主流，數論當然也是。建議數學工作者仔細研讀本書，這樣的書不多

評分☆☆☆☆☆

包裝還行，活動時買的。還沒看，先收藏。

評分☆☆☆☆☆

雖然不太看得懂，這書還是非常的難得！

評分☆☆☆☆☆

此書講瞭很多有意思的東西，值得慢慢品讀，雖然沒看過，但是老師推薦來著