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[法] 赛瑞 著
出版社: 世界图书出版公司 ISBN:9787510005350 版次:1 商品编码:10184600 包装:平装 外文名称:A Course in Arithmetic 开本:24开 出版时间:2009-08-01 用纸:胶版纸 页数:115 正文语种:英语
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
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.
算术教程(英文版) [A Course in Arithmetic] 电子书 下载 mobi epub pdf txt
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☆☆☆☆☆
||
[法] 赛瑞 著
出版社: 世界图书出版公司 ISBN:9787510005350 版次:1 商品编码:10184600 包装:平装 外文名称:A Course in Arithmetic 开本:24开 出版时间:2009-08-01 用纸:胶版纸 页数:115 正文语种:英语
内容简介
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.内页插图
目录
PrefacePart 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.
算术教程(英文版) [A Course in Arithmetic] 电子书 下载 mobi epub pdf txt
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