二次型和 Clifford 群的算术和解析理论（影印版）

样章

作者：

Goro Shimura

定价：

135.00 元

版面字数：

450千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2023年

ISBN：

978-7-04-059298-6

物料号：

59298-00

出版时间：

2023-03-08

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

代数学

暂无

目录
- 前辅文
- Chapter I. Algebraic theory of quadratic forms, Clifford algebras, and spin groups
  - 1. Quadratic forms and associative algebras
  - 2. Clifford algebras
  - 3. Clifford groups and spin groups
  - 4. Parabolic subgroups
- Chapter II. Quadratic forms, Clifford algebras, and spin groups over a local or global field
  - 5. Orders and ideals in an algebra
  - 6. Quadratic forms over a local field
  - 7. Lower-dimensional cases and the Hasse principle
  - 8. Part I. Clifford groups over a local field
  - 8. Part II. Formal Hecke algebras and formal Euler factors
  - 9. Orthogonal, Clifford, and spin groups over a global field
- Chapter III. Quadratic Diophantine equations
  - 10. Quadratic Diophantine equations over a local field
  - 11. Quadratic Diophantine equations over a global field
  - 12. The class number of an orthogonal group and sums of squares
  - 13. Nonscalar quadratic Diophantine equations; Connection with the mass formula; A historical perspective
- Chapter IV. Groups and symmetric spaces over R
  - 14. Clifford and spin groups over R; The case of signature (1, m)
  - 15. The case of signature (2, m)
  - 16. Orthogonal groups over R and symmetric spaces
- Chapter V. Euler products and Eisenstein series on orthogonal groups
  - 17. Automorphic forms and Euler products on an orthogonal group
  - 18. Eisenstein series on Oω
  - 19. Eisenstein series on Oη
  - 20. Arithmetic description of the pullback of an Eisenstein series
  - 21. Analytic continuation of Euler products and Eisenstein series
- Chapter VI. Euler products and Eisenstein series on Clifford groups
  - 22. Euler products on G+(V )
  - 23. Eisenstein series on G(H, 2−1η)
  - 24. Eisenstein series of general types on a Clifford group
  - 25. Euler products for holomorphic forms on a Clifford group
  - 26. Proof of the last main theorem
- Appendix
  - A1. Differential operators on a semisimple Lie group
  - A2. Eigenvalues of integral operators
  - A3. Structure of Clifford algebras over R
  - A4. An embedding of G1(V ) into a symplectic group
  - A5. Spin representations and Lie algebras
- References
- Frequently used symbols
- Index