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

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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.

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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 格式

評分☆☆☆☆☆

這一命題僅僅是這一般規律的一個特殊例子。因此當我們希望錶示整數之間的某個關係——不論涉及的一些特定的整數值如何——是正確的，我們可以用字母a，b，c，…作為錶示整數的符號。於是，我們所熟知的五個算術規律可敘述為：

評分☆☆☆☆☆

很薄，但是有塑封，沒有損壞。書印刷質量正常。

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☆☆☆☆☆

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☆☆☆☆☆

算術的基礎在於：整數的加法和乘法服從某些規律。為瞭要敘述這些具有 普遍性的規律，我們不能用像1，2，3這種錶示特定數的符號。兩個整數，不管它們的次序如何，它們的和相同。而

評分☆☆☆☆☆

短小精悍，名傢經典。

評分☆☆☆☆☆

serre的書，很薄買來看看。

評分☆☆☆☆☆

法國著名數學傢serre的經典之作，數論方麵的初級教材，適閤初學者

評分☆☆☆☆☆

算術的基礎在於：整數的加法和乘法服從某些規律。為瞭要敘述這些具有 普遍性的規律，我們不能用像1，2，3這種錶示特定數的符號。兩個整數，不管它們的次序如何，它們的和相同。而

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