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Tsushima, Ryuji

An explicit dimension formula for the spaces of generalized automorphic forms with respect to \(\mathrm{Sp}(2, \mathbb Z)\). (English) Zbl 0513.10025

Proc. Japan Acad., Ser. A 59, 139-142 (1983).
Reviewer: Masakazu Muro (Gifu)
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Cited in 3 Reviews
Cited in 26 Documents

MSC:

11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

Keywords:

dimension of automorphic cusp forms

Citations:

Zbl 0458.10024; Zbl 0494.10016
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Full Text: DOI

References:

[1] Cartan, H. et al: Seminaire Henri Cartan, 1957/1958, Fonctions Automorphes.
[2] Ise, M.: Generalized automorphic forms and certain holomorphic vector bundles. Amer. J. Math., 86, 70-108 (1964). JSTOR: · Zbl 0137.05801 · doi:10.2307/2373036
[3] Kawamata, Y.: A generalization of Kodaira-Ramanujam’s vanishing theorem. Math. Ann., 261, 43-46 (1982). · Zbl 0476.14007 · doi:10.1007/BF01456407
[4] Nakano, S.: On complex analytic vector bundles. J. Math. Soc. Japan, 7, 1-12 (1955). · Zbl 0068.34403 · doi:10.2969/jmsj/00710001
[5] Namikawa, Y.: A new compactification of the Siegel space and degeneration of abelian varieties. I; II. Math. Ann., 221, 97-141; 201-241 (1976). · Zbl 0327.14013 · doi:10.1007/BF01596390
[6] Tsushima, R.: A formula for the dimension of spaces of Siegel cusp forms of degree three. Amer. J. Math., 102, 937-977 (1980). JSTOR: · Zbl 0458.10024 · doi:10.2307/2374198
[7] Tsushima, R.: On the spaces of Siegel cusp forms of degree two. ibid., 104, 843-885 (1982). JSTOR: · Zbl 0494.10016 · doi:10.2307/2374209
[8] Tsushima, R.: An explicit dimension formula for the spaces of generalized automorphic forms with respect to Sp(2,Z) (to appear). · Zbl 0513.10025 · doi:10.3792/pjaa.59.139
[9] Viehweg, E.: Vanishing theorems. J. reine angew. Math., 335, 1-8 (1982). · Zbl 0485.32019 · doi:10.1515/crll.1982.335.1
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