2000年8月22日 志村五郎 (著)  Arithmeticity in the Theory of Automorphic Forms. Mathematical Surveys and Monographs (Paperback ed.). American Mathematical Society. (2000-08-22). 


Introduction 12 Free
Chapter I. Automorphic Forms and Families of Abelian Varieties 18 Free
1. Algebraic preliminaries 18
2. Polarized abelian varieties 24
3. Symmetric spaces and factors of automorphy 28
4. Families of polarized abelian varieties 33
5. Definition of automorphic forms 41
6. Parametrization by theta functions 48
Chapter II. Arithmeticity of Automorphic Forms 56
7. The field A[sub(0)](Q[sub(ab)]) 56
8. Action of certain elements of G[sub(A)] on R 61
9. The reciprocity-law at CM-points and rationality of automorphic forms 69
10. Automorphisms of the spaces of automorphic forms 78
11. Arithmeticity at CM-points 87
Chapter III. Arithmetic of Differential Operators and Nearly Holomorphic Functions 98
12. Differential operators on symmetric spaces 98
13. Nearly holomorphic functions 109
14. Arithmeticity of nearly holomorphic functions 118
15. Holomorphic projection 133
Chapter IV. Eisenstein Series of Simpler Types 138
16. Eisenstein series on U(η[sub(n)]) 138
17. Arithmeticity and near holomorphy of Eisenstein series 148
18. Eisenstein series in the Hilbert modular case 160
Chapter V. Zeta Functions Associated with Hecke Eigenforms 170
19. Formal Euler products and generalized Möbius functions 170
20. Dirichlet series obtained from Hecke eigenvalues and Fourier coefficients 177
21. The Euler products for the forms of half-integral weight 186
22. The largest possible pole of Z(s, f, x) 188
Chapter VI. Analytic Continuation and Near Holomorphy of Eisenstein Series of General Types 196
23. Eisenstein series of general types 196
24. Pullback of Eisenstein series 205
25. Proof of Theorems in Sections 20 and 23 214
26. Near holomorphy of Eisenstein series in Case UB 219
Chapter VII. Arithmeticity of the Critical Values of Zeta Functions and Eisenstein Series of General Types 230
27. The spaces of holomorphic Eisenstein series 230
28. Main theorems on arithmeticity in Cases SP and UT 241
29. Main theorems on arithmeticity in Case UB 251
Appendix 258
A1. The series associated to a symmetric matrix and Gauss sums 258
A2. Metaplectic groups and factors of automorphy 262
A3. Transformation formulas of general theta series 273
A4. The constant term of a theta series at each cusp depends only on the genus 283
A5. Theta series of a hermitian form 285
A6. Estimate of the Fourier coefficients of a modular form 289
A7. The Mellin transforms of Hilbert modular forms 293
A8. Certain unitarizable representation spaces 296
References

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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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備忘録 メモ

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