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Jacobi-like forms and power series bundles

Published online by Cambridge University Press:  17 April 2009

Min Ho Lee
Min Ho Lee
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, United States of America, e-mail: [email protected]
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Jacobi-like forms are certain formal power series which generalise Jacobi forms in some sense, and they are closely linked to modular forms when their coefficients are holomorphic functions on the Poincaré upper half plane. We construct two types of vector bundles whose fibres are isomorphic to the space of certain formal power series and whose sections can be identified with Jacobi-like forms for a discrete subgroup of SL (2,ℝ).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 2 , October 2002 , pp. 301 - 311
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Berndt, R. and Schmidt, R., Elements of the representation theory of the Jacobi group (Birkhäuser, Boston, 1998).Google Scholar
[2]Borcherds, R., ‘Automorphic forms on O s+2, 2(R) and infinite products’, Invent. Math. 120 (1995), 161–213.CrossRefGoogle Scholar
[3]Cohen, P., Manin, Y. and Zagier, D., ‘Automorphic pseudodifferential operators’, in Algebraic aspects of nonlinear systems (Birkhäuser, Boston, 1997), pp. 17–47.Google Scholar
[4]Eichler, M. and Zagier, D., The theory of Jacobi forms, Progress in Math. 55 (Birkhäuser, Boston, 1985).CrossRefGoogle Scholar
[5]Gritsenko, V., ‘Elliptic genns of Calabi-Yau manifolds and Jacobi and Siegel modular forms’, St. Petersburg Math. J. 11 (2000), 781–804.Google Scholar
[6]Kohnen, W., ‘Jacobi forms and Siegel modular forms: Recent results and problems’, Enseign. Math. 39 (1993), 121–136.Google Scholar
[7]Kramer, J., ‘A geometric approach to the theory of Jacobi forms’, Compositio Math. 79 (1991), 1–19.Google Scholar
[8]Lee, M. H., ‘Jacobi forms on symmetric domains and torus bundles over abeloian schemes’, J. Lie. Theory 11 (2001), 545–557.Google Scholar
[9]Skoruppa, N., ‘Developments in the theory of Jacobi forms’, in Conference on automorphic forms and their applications. Khabarovsk 1988 (Inst. Appl. Math., Khabarovsk, 1990), pp. 167–185.Google Scholar
[10]Wirthmller, K., ‘Root systems and Jacobi forms’, Composito Math. 82 (1992), 293–354.Google Scholar
[11]Zagier, D., ‘Modular forms and differential operators’, Proc. Indian. Acad. Sci. Math. Sci. 104 (1994), 57–75.CrossRefGoogle Scholar