基础数论（英文版） [Basic Number Theory] epub pdf mobi txt 电子书 下载 2025

基础数论（英文版） [Basic Number Theory] epub pdf mobi txt 电子书 下载 2025

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基础数论（英文版） [Basic Number Theory] epub pdf mobi txt 电子书 下载 2025

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内容简介

　　The first part of this volume is based on a course taught at Princeton　University in 1961-62; at that time, an excellent set of notes was prepared　by David Cantor, and it was originally my intention to make these notes　available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by Chevalley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very well. It contained a brief but essentially com- plete account of the main features of classfield theory, both local and global; and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I included such a treatment of this topic. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. In fact, I have adhered to it rather closely at some critical points.

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目录

Chronological table
Prerequisites and notations
Table of notations

PART Ⅰ ELEMENTARY THEORY
Chapter Ⅰ Locally compact fields
1 Finite fields
2 The module in a locally compact field
3 Classification of locally compact fields
4 Structure 0f p-fields

Chapter Ⅱ Lattices and duality over local fields
1 Norms
2 Lattices
3 Multiplicative structure of local fields
4 Lattices over R
5 Duality over local fields

Chapter Ⅲ Places of A-fields
1 A-fields and their completions
2 Tensor-products of commutative fields
3 Traces and norms
4 Tensor-products of A-fields and local fields

Chapter Ⅳ Adeles
1 Adeles of A-fields
2 The main theorems
3 Ideles
4 Ideles of A-fields

Chapter Ⅴ Algebraic number-fields
1， Orders in algebras over Q
2 Lattices over algebraic number-fields
3 Ideals
4 Fundamental sets

Chapter Ⅵ The theorem of Riemann-Roch
Chapter Ⅶ Zeta-functions of A-fields
1 Convergence of Euler products
2 Fourier transforms and standard functions
3 Quasicharacters
4 Quasicharacters of A-fields
5 The functional equation
6 The Dedekind zeta-function
7 L-functions
8 The coefficients of the L-series

Chapter Ⅷ Traces and norms
1 Traces and norms in local fields
2 Calculation of the different
3 Ramification theory
4 Traces and norms in A-fields
5 Splitting places in separable extensions
6 An application to inseparable extensions

PART Ⅱ CLASSFIELD THEORY
Chapter IX Simple algebras
1 Structure of simple algebras
2 The representations of a simple algebra
3 Factor-sets and the Brauer group
4 Cyclic factor-sets
5 Special cyclic factor-sets

Chapter Ⅹ Simple algebras over local fields
1 Orders and lattices
2 Traces and norms
3 Computation of some integrals

Chapter Ⅺ Simple algebras over A-fields
1. Ramification
2. The zeta-function of a simple algebra
3. Norms in simple algebras
4. Simple algebras over algebraic number-fields . .

Chapter Ⅻ. Local classfield theory
1. The formalism of classfield theory
2. The Brauer group of a local field
3. The canonical morphism
4. Ramification of abelian extensions
5. The transfer

Chapter XIII. Global classfield theory
I. The canonical pairing
2. An elementary lemma
3. Hasses "law of reciprocity" .
4. Classfield theory for Q
5. The Hiibert symbol
6. The Brauer group of an A-field
7. The Hilbert p-symbol
8. The kernel of the canonical morphism
9. The main theorems
10. Local behavior of abelian extensions
11. "Classical" classfield theory
12. "Coronidis loco".
Notes to the text
Appendix Ⅰ. The transfer theorem
Appendix Ⅱ. W-groups for local fields
Appendix Ⅲ. Shafarevitchs theorem
Appendix Ⅳ. The Herbrand distribution
Index of definitions

前言/序言

　　The first part of this volume is based on a course taught at PrincetonUniversity in 1961-62; at that time， an excellent set of notes was preparedby David Cantor， and it was originally my intention to make these notesavailable to the mathematical public with only quite minor changes.Then， among some old papers of mine， I accidentally came across along=forgotten manuscript by Chevalley， of pre-war vintage （forgotten，that is to say， both by me and by its author） which， to my taste at least，seemed to have aged very well. It contained a brief but essentially com-plete account of the main features of classfield theory， both local andglobal; and it soon became obvious that the usefulness of the intendedvolume would be greatly enhanced if I included such a treatment of thistopic. It had to be expanded， in accordance with my own plans， but itsoutline could be preserved without much change. In fact， I have adheredto it rather closely at some critical points.
　　To improve upon Hecke， in a treatment along classical lines of thetheory of algebrai~ numbers， would be a futile and impossible task. Aswill become apparent from the first pages of this book， I have rathertried to draw the conclusions from the developments of the last thirtyyears， whereby locally compact groups， measure and integration havebeen seen to play an increasingly important role in classical number-theory. In the days of Dirichlet and Hermite， and even of Minkowski，the appeal to "continuous variables" in arithmetical questions may wellhave seemed to come out of some magicians bag of tricks. In retrospect，we see now that the real numbers appear there as one of the infinitelymany completions of the prime field， one which is neither more nor lessinteresting to the arithmetician than its p=adic companions， and thatthere is at least one language and one technique， that of the adeles， for bringing them all together under one roof and making them cooperate for a common purpose. It is needless here to go into the history of thesedevelopments; suffice it to mention such names as Hensel， Hasse， Chevalley， Artin; every one of these， and more recently Iwasawa， Tate， Tamagawa， helped to make some significant step forward along this road. Once the presence of the real field， albeit at infinite distance， ceases to be regarded as a necessary ingredient in the arithmeticians brew.

基础数论（英文版） [Basic Number Theory] epub pdf mobi txt 电子书 下载 2025

基础数论（英文版） [Basic Number Theory] 下载 epub mobi pdf txt 电子书 2025

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数论就是指研究整数性质的一门理论。数论=绝大部分算术（少数例外）。不过通常算术指数的计算，数论指数的理论。整数的基本元素是素数，所以数论的本质是对素数性质的研究。它与平面几何同是历史悠久的学科。按研究方法来看，数论大致可分为初等数论和高等数论。初等数论是用初等方法研究的数论，它的研究方法本质上说，就是利用整数环的整除性质，主要包括整除理论、同余理论、连分数理论，其中最高成就包括高斯的“二次互反律”等。高等数论则包括了更为深刻的数学研究工具。它大致包括代数数论、解析数论、计算数论等等。

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cjmroh基础数论（英文版）

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中国

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问题

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门类

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weil的书 那必须赞啊

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In fact, I have adhered to it rather closely at some critical points.（引用自原文）

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同上所述， 初等数论主要就是研究整数环的整除理论及同余理论。此外它也包括了连分数理论和少许不定方程的问题。本质上说，初等数论的研究手段局限在整除性质上。

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要很好的基础，推荐给大家

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