算术教程 azw3 chm 地址 kindle 阿里云 下载 umd pdf

《算术教程(英文版)》讲述了：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.

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

暂无相关内容，正在全力查找中

暂无出版社相关信息，正在全力查找中！

暂无相关书籍摘录，正在全力查找中！

在线阅读地址：算术教程在线阅读

在线听书地址：算术教程在线收听

在线购买地址：算术教程在线购买

暂无原文赏析，正在全力查找中！

书籍介绍

《算术教程(英文版)》讲述了：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.