Primes of the Form X2+ny2 pdf epub mobi txt 电子书下载 2025

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DAVID A. COX, PhD, is William J. Walker Professor of Mathematics in the Department of Mathematics at Amherst College.

出版者:John Wiley & Sons Inc

作者:David A. Cox

出品人:

页数:378

译者:

出版时间:2013-4-22

价格:0

装帧:Paperback

isbn号码:9781118390184

丛书系列:Pure and Applied Mathematics: A Wiley Series of Texts, Monographs, and Tracts

图书标签:

数学
Algebra
代数数论
代数
二次型
Cox
英文
数论

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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.

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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...

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其实只能读懂前两章

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其实只能读懂前两章

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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

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其实只能读懂前两章