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Construction of mixed automorphic forms

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  09 April 2009

Youngju Choie
Youngju Choie
Affiliation:
Department of Mathematics Pohang University of Science and TechnologyPohangKorea790-784 e-mail: [email protected]
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Abstract

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It has been known that mixed automorphic forms arise naturally as holomorphic forms on elliptic varieties and that they include classical automorphic forms as a special case. In this paper, we show how to construct mixed automorphic forms of type (k, l) from elliptic modular forms to give nontrivial examples of mixed automorphic forms.

MSC classification

Secondary: 11F55: Other groups and their modular and automorphic forms (several variables) 11F60: Hecke-Petersson operators, differential operators (several variables)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 3 , December 1997 , pp. 390 - 395
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Hunt, B. and Meyer, W., ‘Mixed automorphic forms and invariants of elliptic surfaces’, Math. Ann. 271 (1985), 53–80.CrossRefGoogle Scholar
[2]Lee, M. H., ‘Mixed cusp forms and holomorphic forms on elliptic varieties’, Pacific. J. Math. 132 (1988), 363–370.CrossRefGoogle Scholar
[3]Lee, M. H., ‘Periods of mixed cusp forms’, Manuscripta Math. 73 (1991), 163–177.CrossRefGoogle Scholar
[4]Lee, M. H., ‘Mixed cusp forms and Poincaré series’, Rocky Mountain J. Math. 23 (1993), 1009–1022.CrossRefGoogle Scholar
[5]Lee, M. H., ‘Mixed Siegel modular forms and Kuga fiber varieties’, Illinois J. Math. 38 (1994), 692–700.Google Scholar
[6]Lee, M. H., ‘Rational structures on mixed cusp forms’, Panamer. Math. J. 4 (1994), 81–100.Google Scholar
[7]Lee, M. H., ‘Mixed automorphic vector bundles on Shimura varieties’, Pacific J. Math. 173 (1996), 105–126.Google Scholar
[8]Miyake, T., Modular forms (Springer, Heidelberg, 1989).CrossRefGoogle Scholar
[9]Stiller, P., Special values of Dirichlet series, monodromy, and the periods of automorphic forms, Mem. Amer. Math. Soc., 299 (Amer. Math. Soc., Providence, 1984).Google Scholar