Primes of the Form X2+ny2 pdf epub mobi txt 电子书 下载 2025
- 数学
- Algebra
- 代数数论
- 代数
- 二次型
- Cox
- 英文
- 数论
- 数论
- 素数
- 二次型
- 丢番图方程
- 代数数论
- 模形式
- 椭圆曲线
- 费马大定理
- 高斯整数
- 算术几何
具体描述
Written for readers with modest mathematical backgrounds, this book contains numerous exercises and examples at varied levels and provides a well-motivated introduction to the classical formulation of class field theory--placing great importance on the explicit numerical example to illustrate the power of basic theorems in various situations. It includes an elementary treatment of quadratic forms and genus theory; addresses when a prime p is of the form x2+ny2; features new coverage of Shimura reciprocity law; and includes simultaneous treatment on elementary and advanced aspects of number theory.
作者简介
DAVID A. COX, PhD, is William J. Walker Professor of Mathematics in the Department of Mathematics at Amherst College.
目录信息
Preface to the Second Edition xi
Notation xiii
Introduction 1
Chapter One: From Fermat to Gauss
Chapter Two: Class Field Theory
Chapter Three: Complex Multiplication
Chapter Four: Additional Topics
Refrences
Additional References
Index
· · · · · · (收起)
读后感
Bhargava写过论文<higher composition laws>，就是以 Gauss composition,为基础，构造higher analogues of Gauss composition,以探索在其他代数环（域）上相似结构的可能。Gauss composition 是理解 二次域上的ideal class groups的最好方式，而这些similar laws of comp...
评分Bhargava写过论文<higher composition laws>，就是以 Gauss composition,为基础，构造higher analogues of Gauss composition,以探索在其他代数环（域）上相似结构的可能。Gauss composition 是理解 二次域上的ideal class groups的最好方式，而这些similar laws of comp...
评分Bhargava写过论文<higher composition laws>，就是以 Gauss composition,为基础，构造higher analogues of Gauss composition,以探索在其他代数环（域）上相似结构的可能。Gauss composition 是理解 二次域上的ideal class groups的最好方式，而这些similar laws of comp...
评分Bhargava写过论文<higher composition laws>，就是以 Gauss composition,为基础，构造higher analogues of Gauss composition,以探索在其他代数环（域）上相似结构的可能。Gauss composition 是理解 二次域上的ideal class groups的最好方式，而这些similar laws of comp...
评分Bhargava写过论文<higher composition laws>，就是以 Gauss composition,为基础，构造higher analogues of Gauss composition,以探索在其他代数环（域）上相似结构的可能。Gauss composition 是理解 二次域上的ideal class groups的最好方式，而这些similar laws of comp...
用户评价
是class field theory最好的入门书，neukirch也有相关方面的两本书，一本<<algebraic number theory>>和<<class field theory>>但观点很高也很抽象。这本每章都为了解决一个数论问题而开始，把读者一步步引到谜底，具体的逐渐融合进抽象的框架里。这本书的第三四章讲的是complex multiplication,elliptic curve,shimura reciprocity这些主题跟modular forms 有关。感叹一下everywhere is modular forms.想更深入的话可以分别看neukirch和shimura的书
评分是class field theory最好的入门书，neukirch也有相关方面的两本书，一本<<algebraic number theory>>和<<class field theory>>但观点很高也很抽象。这本每章都为了解决一个数论问题而开始，把读者一步步引到谜底，具体的逐渐融合进抽象的框架里。这本书的第三四章讲的是complex multiplication,elliptic curve,shimura reciprocity这些主题跟modular forms 有关。感叹一下everywhere is modular forms.想更深入的话可以分别看neukirch和shimura的书
评分是class field theory最好的入门书，neukirch也有相关方面的两本书，一本<<algebraic number theory>>和<<class field theory>>但观点很高也很抽象。这本每章都为了解决一个数论问题而开始，把读者一步步引到谜底，具体的逐渐融合进抽象的框架里。这本书的第三四章讲的是complex multiplication,elliptic curve,shimura reciprocity这些主题跟modular forms 有关。感叹一下everywhere is modular forms.想更深入的话可以分别看neukirch和shimura的书
评分其实只能读懂前两章
评分其实只能读懂前两章
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