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

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

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

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] epub pdf mobi txt 電子書 下載 2025

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

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。

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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。

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