The ring of quasimodular forms for a cocompact group |
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Authors: | Najib Ouled Azaiez |
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Institution: | Max Planck Institute für Mathematik, Vivatsagsse 7, D-53111 Bonn, Germany |
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Abstract: | We describe the additive structure of the graded ring of quasimodular forms over any discrete and cocompact group Γ⊂PSL(2,R). We show that this ring is never finitely generated. We calculate the exact number of new generators in each weight k. This number is constant for k sufficiently large and equals where I and are the ideals of modular forms and quasimodular forms, respectively, of positive weight. We show that is contained in some finitely generated ring of meromorphic quasimodular forms with i.e., the same order of growth as ![View the MathML source View the MathML source](http://ars.els-cdn.com/content/image/1-s2.0-S0022314X07001862-si8.gif) |
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Keywords: | Quasimodular forms Modular groups |
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