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QUASIMODULAR FORMS AND VECTOR BUNDLES

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  02 July 2009

MIN HO LEE
MIN HO LEE*
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, USA (email: [email protected])
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Abstract

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Modular forms for a discrete subgroup Γ of SL(2,ℝ) can be identified with holomorphic sections of line bundles over the modular curve U corresponding to Γ, and quasimodular forms generalize modular forms. We construct vector bundles over U whose sections can be identified with quasimodular forms for Γ.

Keywords

quasimodular formsmodular formsvector bundles

MSC classification

Secondary: 11F11: Holomorphic modular forms of integral weight
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 3 , December 2009 , pp. 402 - 412
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

References

[1]Choie, Y. and Lee, M. H., ‘Quasimodular forms, Jacobi-like forms, and pseudodifferential operators’, Preprint.Google Scholar
[2]Eskin, A. and Okounkov, A., ‘Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials’, Invent. Math. 145 (2001), 59–103.CrossRefGoogle Scholar
[3]Kaneko, M. and Zagier, D., A Generalized Jacobi Theta Function and Quasimodular Forms, Progress in Mathematics, 129 (Birkhäuser, Boston, 1995), pp. 165–172.Google Scholar
[4]Okounkov, A. and Pandharipande, R., ‘Gromov–Witten theory, Hurwitz theory, and completed cycles’, Ann. of Math. 163 (2006), 517–560.CrossRefGoogle Scholar
[5]Royer, E., ‘Evaluating convolution sums of the divisor function via quasimodular forms’, Int. J. Number Theory 21 (2007), 231–262.CrossRefGoogle Scholar