算術教程（英文版） [A Course in Arithmetic] pdf epub mobi txt 電子書 下載 2025

簡體網頁||繁體網頁

☆☆☆☆☆

[法] 賽瑞 著

齣版社： 世界圖書齣版公司

ISBN：9787510005350

版次：1

商品編碼：10184600

包裝：平裝

外文名稱：A Course in Arithmetic

開本：24開

齣版時間：2009-08-01

用紙：膠版紙

頁數：115

正文語種：英語

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.

評分☆☆☆☆☆

短小精悍，名傢經典。

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☆☆☆☆☆

　　讀者對象：數學專業的高年級本科生、研究生和相關專業的學者本書主要講述具有一般係數體係拓撲空間的上同調理論。層論包括對代數拓撲很重要的領域。書中有好多創新點，引進不少新概念，全書內容貫穿一緻。證實瞭廣義同調空間中層理論上同調滿足同調基本特性的事實。將相對上同調引入層理論中。

評分☆☆☆☆☆

自然數或正整數的數學理論就是眾所周知的算術.至於幾何、 代數等許多數學分支學科的名稱，都是後來很晚的時候纔有的。

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☆☆☆☆☆

很棒

評分☆☆☆☆☆

看看歪果仁怎麼講算術。

評分☆☆☆☆☆

算術教程（英文版），很不錯的好書，和期待。

評分☆☆☆☆☆

1+2=2+1