《算術教程》是2009年8月1日世界圖書出版公司出版的圖書，作者是（法）賽瑞（Jean-Pierre Serre）。
基本介紹
- 書名：算術教程
- 作者：（法）賽瑞（Jean-Pierre Serre）
- 原作品：A Course in Arithmetic
- 出版社：世界圖書出版公司
- 出版時間：2009年8月1日
- 開本：24 開
- ISBN：7510005353, 9787510005350
- 版次：1
- 正文語種：英語
內容簡介,目錄,
內容簡介
《算術教程(英文版)》講述了：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.
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 Ⅲ 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 Ⅶ 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
