2004年3月1日 志村五郎 (著)  Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups. Mathematical Surveys and Monographs (Hardcover ed.). American Mathematical Society. (2004-03-01). 


Introduction 12 Free
Chapter I. Algebraic theory of quadratic forms, Clifford algebras, and spin groups 20 Free
1. Quadratic forms and associative algebras 20
2. Clifford algebras 26
3. Clifford groups and spin groups 31
4. Parabolic subgroups 39
Chapter II. Quadratic forms, Clifford algebras, and spin groups over a local or global field 48
5. Orders and ideals in an algebra 48
6. Quadratic forms over a local field 56
7. Lower-dimensional cases and the Hasse principle 63
8. Part I. Clifford groups over a local field 73
8. Part II. Formal Hecke algebras and formal Euler factors 83
9. Orthogonal, Clifford, and spin groups over a global field 91
Chapter III. Quadratic Diophantine equations 104
10. Quadratic Diophantine equations over a local field 104
11. Quadratic Diophantine equations over a global field 112
12. The class number of an orthogonal group and sums of squares 124
13. Nonscalar quadratic Diophantine equations; Connection with the mass formula; A historical perspective 137
Chapter IV. Groups and symmetric spaces over R 150
14. Clifford and spin groups over R; The case of signature (1,m) 150
15. The case of signature (2,m) 157
16. Orthogonal groups over R and symmetric spaces 165
Chapter V. Euler products and Eisenstein series on orthogonal groups 174
17. Automorphic forms and Euler products on an orthogonal group 174
18. Eisenstein series on o[sup(w)] 184
19. Eisenstein series on o[sup(η)] 192
20. Arithmetic description of the pullback of an Eisenstein series 198
21. Analytic continuation of Euler products and Eisenstein series 207
Chapter VI. Euler products and Eisenstein series on Clifford groups 216
22. Euler products on G[sup(+)](V) 216
23. Eisenstein series on G(H, 2[sup(…1)]η) 223
24. Eisenstein series of general types on a Clifford group 229
25. Euler products for holomorphic forms on a Clifford group 237
26. Proof of the last main theorem 245
Appendix 254
A1. Differential operators on a semisimple Lie group 254
A2. Eigenvalues of integral operators 261
A3. Structure of Clifford algebras over R 272
A4. An embedding of G[sup(1)](v) into a symplectic group 276
A5. Spin representations and Lie algebras 279
References 283
Frequently used symbols
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志村五郎 (著)  Shimura, Goro 書籍 英語版


志村五郎 (著)   Automorphic Functions and Number Theory. Lecture Notes in Mathematics. 54 (Paperback ed.). Springer. (1968).


志村五郎 (著) Introduction to the Arithmetic Theory of Automorphic Functions (Paperback ed.). Princeton University Press. (1971-08-01). 


志村五郎 (著)  Euler Products and Eisenstein Series. CBMS Regional Conference Series in Mathematics (Paperback ed.). American Mathematical Society. (1997-07-01). 


志村五郎 (著)  Abelian Varieties with Complex Multiplication and Modular Functions (Hardcover ed.). Princeton University Press. (1997-12-08).


志村五郎 (著)  Arithmeticity in the Theory of Automorphic Forms. Mathematical Surveys and Monographs (Paperback ed.). American Mathematical Society. (2000-08-22). 


志村五郎 (著)  Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups. Mathematical Surveys and Monographs (Hardcover ed.). American Mathematical Society. (2004-03-01). 


志村五郎 (著) Elementary Dirichlet Series and Modular Forms. Springer Monographs in Mathematics (Paperback ed.). Springer New York. (2009-12-28). 



志村五郎 (著)  Arithmetic of Quadratic Forms. Springer Monographs in Mathematics (Hardcover ed.). Springer. (2010-07-15). 

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論文集

Collected Papers. I: 1954-1965 (Hardcover ed.). Springer. (2002). 

Collected Papers. II: 1967-1977 (Hardcover ed.). Springer. (2002). 

Collected Papers. III: 1978-1988 (Hardcover ed.). Springer. (2003). 

Collected Papers. IV: 1989-2001 (Hardcover ed.). Springer. (2003). 

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