內容簡介
The first one is purely algebraic. Its objective is the classification ofquadratic forms over the field of rational numbers (Hasse-Minkowskitheorem). It is achieved in Chapter IV. The first three chapters contain somepreliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols.Chapter V applies the preceding results to integral quadratic forms indiscriminant + 1. These forms occur in various questions: modular functions,differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor-phic functions). Chapter VI gives the proof of the "theorem on arithmeticprogressions" due to Dirichlet; this theorem is used at a critical point in thefirst part (Chapter 111, no. 2.2). Chapter VII deals with modular forms,and in particular, with theta functions. Some of the quadratic forms ofChapter V reappear here.
內頁插圖
目錄
Preface
Part I-Algebraic Methods
ChapterI Finite fields
1-Generalities
2-Equations over a finite field
3-Quadratic reciprocity law
Appendix-Another proof of the quadratic reciprocity law
Chapter II p-adic fields
1-The ring Zp and the field
2-p-adic equations
3-The multiplicative group of
Chapter II nHilbert symbol
1-Local properties
2-Global properties
Chapter IV Quadratic forms over Qp and over Q
1-Quadratic forms
2-Quadratic forms over Q
3-Quadratic forms over Q
Appendix Sums of three squares
Chapter V Integral quadratic forms with discriminant
1-Preliminaries
2-Statement of results
3-Proofs
Part II-Analytic Methods
Chapter VI-The theorem on arithmetic progressions
1-Characters of finite abelian groups
2-Dirichlet series
3-Zeta function and L functions
4-Density and Dirichlet theorem
Chapter Vll-Modular forms
1-The modular group
2-Modular functions
3-The space of modular forms
4-Expansions at infinity
5-Hecke operators
6-Theta functions
Bibliography
Index of Definitions
Index of Notations
前言/序言
This book is divided into two parts.
The first one is purely algebraic. Its objective is the classification ofquadratic forms over the field of rational numbers (Hasse-Minkowskitheorem). It is achieved in Chapter IV. The first three chapters contain somepreliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols.Chapter V applies the preceding results to integral quadratic forms indiscriminant + 1. These forms occur in various questions: modular functions,differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor-phic functions). Chapter VI gives the proof of the "theorem on arithmeticprogressions" due to Dirichlet; this theorem is used at a critical point in thefirst part (Chapter 111, no. 2.2). Chapter VII deals with modular forms,and in particular, with theta functions. Some of the quadratic forms ofChapter V reappear here.
The two parts correspond to lectures given in 1962 and 1964 to secondyear students at the Ecole Normale Superieure. A redaction of these lecturesin the form of duplicated notes, was made by J.-J. Saosuc (Chapters l-IV)and J.-P. Ramis and G. Ruget (Chapters VI-VIi). They were very useful tome; I extend here my gratitude to their authors.
算術教程(英文版) [A Course in Arithmetic] 下載 mobi epub pdf txt 電子書
評分
☆☆☆☆☆
書很好,發貨快,很滿意。這本書書很好!推薦大傢都看看!收到非常欣喜!快遞一天就到瞭!支持京東!
評分
☆☆☆☆☆
非常好的一本書,大贊?
評分
☆☆☆☆☆
很不錯,很喜歡,物流給力
評分
☆☆☆☆☆
商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!商品不錯!
評分
☆☆☆☆☆
本書隻有100多頁,但內容很有深度,介紹瞭現代數論的基礎知識,是serre的代錶作之一,如果覺得簡單,可以再看看weil的書。
評分
☆☆☆☆☆
開捲有益處,不忘送書人
評分
☆☆☆☆☆
算術教程(英文版),很不錯的好書,和期待。
評分
☆☆☆☆☆
這一命題僅僅是這一般規律的一個特殊例子。因此當我們希望錶示整數之間的某個關係——不論涉及的一些特定的整數值如何——是正確的,我們可以用字母a,b,c,…作為錶示整數的符號。於是,我們所熟知的五個算術規律可敘述為:
評分
☆☆☆☆☆
正在閱讀中。。。。。。