Abstract
Let⌈be a subgroup of the modular groupPSL(2,Z) then⌈acts on the upper half planeH={zЄC: Imz> 0} and we can form the Riemann surfaceM=H/⌈, see [3]. The complex line bundles on a Riemann surfaceMform a groupH1(M,*), see [4], and whenever we raise a line bundle to a power it will be in this group. Letκdenote the canonical bundle onMthen a modular form of weightνis a section of the bundle. A modularn-jet is then a section ofJnthen-th jet bundle, see [7]. We can reformulate these ideas in the following terms. A modular form can be viewed as a functionΦ: H→Cand a modularn-jet as a vector valued functionΦ: H → Cn+1both of which satisfy a transformation law under the elements ofΓ.
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