- 二次互反律的傅里叶分析证明(英文)/国外优秀数学著作原版系列
- - 作者：(美)迈克尔·C.贝格|责编:李广鑫//杜莹雪
  - 出版社：哈尔滨工业大学
  - ISBN：9787560389240
  - 出版日期：2020/07/01
  - 页数：220
- 售价：19.2

内容大纲
本书是一本英文原版影印版专著，二次剩余的概念最早出现于欧拉1754年发表的论文中，1783年欧拉明确地叙述了二次互反律，二次互反律的各种角度的推广是构成近代数论的一项重要内容。本书主要包括二次互反律的赫克证明、高斯和、相对二次互反律、诺依曼定理、局部紧致阿贝尔情形、海森堡群、酉算子群、π的核心、局部域的矢量空间、局部域的四元法、久保田和上同调、辛群的双面、希尔伯特互反律等内容。本书适合二次互反律专业的大学生或研究生参考阅读。
作者介绍
目录
PREFACE
ACKNOWLEDGMENTS
INTRODUCTION
1. Hecke's Proof of Quadratic Reciprocity
  1.1 Hecke 9-functions and Their Functional Equation
  1.2 Gauss(-Hecke) Sums
  1.3 Relative Quadratic Reciprocity
  1.4 Endnotes to Chapter 1
2.Two Equivalent Forms of Quadratic Reciprocity
3.The Stone-Von Neumann Theorem
  3.1 The Finite Case:A Paradigm
  3.2 The Locally Compact Abelian Case: Some Remarks
  3.3 The Form of the Stone-Von Neumann Theorem Used
  in 8 4
4.Weil's"Acta"Paper
  4.1 Heisenberg Groups
  4.2 A Heisenberg Group and A Group of Unitary
  Operators
  4.3 The Kernel of T
  4.4 Second-Degree Characters
  4.5 The Splitting of T on a Distinguished Subgroup of
  B(G)
  4.6 Vector Spaces Over Local Fields
  4.7 Quaternions Over a Local Field
  4.8 Hilbert Reciprocity
  4.9 The Stone-Von Neumann Theorem Revisited
  4.10 The Double Cover of the Symplectic Group
  4.11 Endnotes to Chapter 4
5.Kubota and Cohomology
  5.1 Weil Revisited
  5.2 Kubota's Cocycle
  5.3 The Splitting of a Over SL(2,k)
  5.4 2-Hilbert Reciprocity Once Again
6.The Algebraic Agreement Between the Formalisms of Weil
  and Kubota
  6.1 The Gruesome Diagram
  6.2 The Even More Gruesome Diagram
  7.Hecke's Challenge: General Reciprocity and Fourier
  Analysis on the March
BIBLIOGRAPHY
INDEX
编辑手记

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作者介绍

目录

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