p-adic measures attached to Siegel modular forms

Annales de l'Institut Fourier

Volumn 50, Issue 5, 2000, Pages 1375-1443

  Bocherer S ^a   Schmidt, C G ^b  

^a Mathematisches Institut II ^*  (Germany)

^b UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

p adic interpolation; Siegel modular forms; Standard L functions

Indexed keywords

EID: 0034550954     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.1796     Document Type: Article

References (38)

1. A.N. ANDRIANOV, V.L. KALININ, On the analytic properties of standard zeta functions of Siegel modular forms, Math. USSR Sbornik, 35 (1979), 1-17.
2. A.N. ANDRIANOV, Quadratic Forms and Hecke Operators. Grundlehren der mathematischen Wissenschaften 286, Berlin-Heidelberg-New York, Springer, 1987.
3. S. BÖCHERER, Über die Fourier-Jacobi-Entwicklung der Siegelschen Eisensteinreihen, Math.Z., 183 (1983), 21-43.
4. S. BÖCHERER, Über die Fourier-Jacobi-Entwicklung der Siegelschen Eisensteinreihen II, Math.Z., 189 (1985), 81-100.
5. S. BÖCHERER, Über die Fourierkoeffizienten Siegelscher Eisensteinreihen, Manuscripta Math., 45 (1984), 273-288.
6. S. BÖCHERER, Über die Funktionalgleichung automorpher L-Funktionen zur Siegelschen Modulgruppe, J. reine angew. Math., 362 (1985), 146-168.
7. S. BÖCHERER, Ein Rationalitätssatz für formale Heckereihen zur Siegelschen Modulgruppe, Abh. Math. Sem. Univ. Hamburg, 56 (1986), 35-47.
8. U. CHRISTIAN, Selberg's Zeta-, L-, and Eisenstein Series. Lecture Notes in Math. 1030. Berlin-Heidelberg-New York, Springer, 1983.
9. U. CHRISTIAN, Maaßsche L-Reihen und eine Identität für Gaußsche Summen, Abh. Math. Sem. Univ. Hamburg, 54 (1984), 163-175.
10. P. DELIGNE, Valeurs de fonctions L et périodes d'intégrales, Proc. Symp Pure Math., 33, Part 2 (1979), 313-346.
11. P. FEIT, Poles and residues of Eisenstein series for symplectic and unitary groups, Memoirs AMS, 61 (1986), no 346.
12. E. FREITAG, Siegelsche Modulfunktionen. Grundlehren der mathematischen Wissenschaften 254, Berlin-Heidelberg-New York, 1983.
13. P.B. GARRETT, M. HARRIS, Special values of triple product L-functions, Amer. J. Math., 115 (1993), 159-238.
14. S. GELBART, I. PIATETSKI-SHAPIRO, S. RALLIS, Explicit Constructions of Automorphic L-Functions. Springer Lecture Notes in Math. 1254, Berlin-Heidelberg-New York, Springer, 1987.
15. M. HARRIS, Special values of zeta functions attached to Siegel modular forms, Ann Sci. Ecole Norm. Sup., 14 (1981), 77-120.
16. L.K. HUA, Harmonic analysis of functions of several complex variables in the classical domains, Transl. Math. Monographs 6, AMS 1963.
17. Y. KITAOKA, Dirichlet series in the theory of Siegel modular forms, Nagoya Math. J., 95 (1984), 73-84.
18. H. MAAß, Siegel's modular forms and Dirichlet series, Lecture Notes in Math. 216, Berlin-Heidelberg-New York, Springer, 1971.
19. Sh.-I. MIZUMOTO, Poles and residues of standard L-functions attached to Siegel modular forms, Math. Ann., 289 (1991), 589-612.
20. A.A. PANCHISHKIN, Non-Archimedean L-Functions of Siegel and Hubert Modular Forms. Springer Lecture Notes in Math. 1471, Berlin-Heidelberg-New York, Springer, 1991.
21. A.A. PANCHISHKIN, Admissible Non-Archimedean Standard Zeta Functions associated with Siegel Modular Forms, Proc. Symp. Pure Math., 55, Part 2, 251-292.
22. I. PIATETSKI-SHAPIRO, S. RALLIS, A new way to get Euler products, J. reine angew. Math., 392 (1988), 110-124.
23. C.G. SCHMIDT, P-adic measures attached to automorphic representations of Gl(3), Invent. Math., 92 (1988), 597-631.
24. G. SHIMURA, On the Fourier coefficients of modular forms of several variables, Nachr. Akad. Wiss. Göttingen, 1975, 261-268.
25. G. SHIMURA, The special values of the zeta functions associated with cusp forms, Comm. Pure Appl. Math., XXIX (1976), 783-804.
26. G. SHIMURA, Arithmetic of differential operators on symmetric domains, Duke Math. J., 48 (1981), 813-843.
27. G. Shimura - , Confluent hypergeometric functions on tube domains, Math. Ann., 269 (1982), 269-302.
28. G. SHIMURA, On Eisenstein Series, Duke Math. J., 50 (1983), 417-476.
29. G. SHIMURA, On differential operators attached to certain representations of classical groups, Invent. Math., 77 (1984), 463-488.
30. G. SHIMURA, Differential operators and the singular values of Eisenstein series, Duke Math. J., 51 (1984), 261-329.
31. G. SHIMURA, On Eisenstein series of half-integral weight, Duke Math. J., 52 (1985), 281-314.
32. G. SHIMURA, On a class of nearly holomorphic automorphic forms, Annals of Math., 123 (1986), 347-406.
33. G. SHIMURA, Nearly holomorphic functions on hermitian symmetric spaces, Math. Ann., 278 (1987), 1-28.
34. G. SHIMURA, Invariant differential operators on hermitian symmetric spaces, Annals of Math., 132 (1990), 237-272.
35. G. SHIMURA, Differential Operators, Holomorphic Projection, and Singular Forms, Duke Math. J., 76 (1994), 141-173.
36. J. STURM, The critical values of zeta functions associated to the symplectic group, Duke Math. J., 48 (1981), 327-350.
37. T. TAMAGAWA, On the zeta functions of a division algebra, Annals of Math., 77 (1963), 387-405.
38. L. WASHINGTON, Introduction to Cyclotomic Fields, Graduate Texts in Math. 83, Berlin-Heidelberg-New York, Springer, 1982.