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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☆☆☆☆☆

算術是數學的一個分支，其內容包括自然數和在各種運算下産生的性質，運算法則以及在實際中的應用。可是，在數學發展的曆史中算術的含義要廣泛得多。

評分☆☆☆☆☆

前兩個是加法和乘法的交換律，它說明人們可以交換加法或乘法中元素的次序。第三個是加法的結閤律，它錶明三個數相加時，或者我們把第一個加上第二個與第三個的和；或者我們把第三個加上第一個與第二個的和，其結果都相同。第四個是乘法的結閤律。最後一個是分配律，它錶明用一個整數去乘一個和時，我們可以用這整數去乘這和的每一項，然後把這些乘積加起來。

評分☆☆☆☆☆

國外係統地整理前人數學知識的書，要算是希臘的歐幾裏得的《幾何原本》最早。《幾何原本》全書共十五捲，後兩捲是後人增補的。全書大部分是屬於幾何知識，在第七、八、九捲中專門討論瞭數的性質和運算，屬於算術的內容。

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☆☆☆☆☆

　　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☆☆☆☆☆

作者太有名，買來先放著，以後再拜讀之

評分☆☆☆☆☆

算術演變

評分☆☆☆☆☆

算術演變

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