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Differential equations for automorphic forms in several complex variables. (English) Zbl 0189.09901


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[1] Aldo Andreotti and Hans Grauert, Algebraische Körper von automorphen Funktionen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1961 (1961), 39 – 48 (German). · Zbl 0096.28001
[2] Hel Braun and Max Koecher, Jordan-Algebren, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band 128, Springer-Verlag, Berlin-New York, 1966 (German). · Zbl 0145.26001
[3] A. Hurwitz, Ueber die Differentialgleichungen dritter Ordnung, welchen die Formen mit linearen Transformationen in sich genügen, Math. Ann. 33 (1889), no. 3, 345 – 352 (German). · JFM 21.0479.01 · doi:10.1007/BF01443965
[4] Jun-ichi Igusa, On Siegel modular forms of genus two, Amer. J. Math. 84 (1962), 175 – 200. · Zbl 0133.33301 · doi:10.2307/2372812
[5] C. G. J. Jacobi, “Über die Differentialgleichung, welcher die Reihen \( 1 \pm 2q + 2{q^4} + \operatorname{etc} .,\;2\sqrt[4]{q} + 2\sqrt[4]{{{q^9}}} + 2\sqrt[4]{{{q^{25}}}} + \operatorname{etc} .\) genüge leisten,” in Gesammelte Werke. Band 2, Springer-Verlag, Berlin, pp. 171-190; Cf. J. Reine Angew. Math. 36 (1848), 97-112.
[6] M. Koecher, Jordan algebras and their applications, Lecture notes, University of Minnesota, Minneapolis, Minn., 1962. · Zbl 0128.03101
[7] Adam Korányi and Joseph A. Wolf, Realization of hermitian symmetric spaces as generalized half-planes, Ann. of Math. (2) 81 (1965), 265 – 288. · Zbl 0137.27402 · doi:10.2307/1970616
[8] R. A. Rankin, The construction of automorphic forms from the derivatives of a given form, J. Indian Math. Soc. (N.S.) 20 (1956), 103 – 116. · Zbl 0072.08601
[9] R. A. Rankin, The construction of automorphic forms from the derivatives of given forms, Michigan Math. J. 4 (1957), 181 – 186. · Zbl 0085.30002
[10] Reinhold Remmert, Meromorphe Funktionen in kompakten komplexen Räumen, Math. Ann. 132 (1956), 277 – 288 (German). · Zbl 0072.08001 · doi:10.1007/BF01360043
[11] H. L. Resnikoff, On differential operators and automorphic forms, Trans. Amer. Math. Soc. 124 (1966), 334 – 346. · Zbl 0148.32504
[12] H. L. Resnikoff, Non trivial cusp forms in several complex variables, Rice Univ. Studies 54 (1968), no. 4, 55 – 61. · Zbl 0198.11402
[13] -, On singular automorphic forms in several complex variables, Amer. J. Math. (to appear)
[14] Carl Ludwig Siegel, Meromorphe Funktionen auf kompakten analytischen Mannigfaltigkeiten, Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. IIa. 1955 (1955), 71 – 77 (German). · Zbl 0064.08201
[15] W. Thimm, Uber die algebraischen Relationen zwischen meromorphen Funktionen in abgeschlossenen Räumen, Dissertation, Konigsberg, 1939.
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