二次型和Clifford群的算术和解析理论(影印版)
作者: Goro Shimura
出版时间:2023-03
出版社:高等教育出版社
- 高等教育出版社
- 9787040592986
- 1版
- 458695
- 46254103-8
- 精装
- 16开
- 2023-03
- 450
- 275
- 数学类
- 本科 研究生及以上
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