We show that the image of repeated differentiation on weak cusp forms is
precisely the subspace which is orthogonal to the space of weakly holomorphic
modular forms. This gives a new interpretation of the weakly holomorphic Hecke
eigenforms

Bringmann, Kathrin

Kane, Ben

Journal of Physics A Mathematical and Theoretical

English

arXiv

Kölner UniversitätsPublikationsServer

Regularized inner products and weakly holomorphic Hecke eigenforms

An interpretation of Guerzhoy's integral weight weakly holomorphic Hecke eigenforms via regularized inner products is given in this paper. In particular, Guerzhoy's eigenforms are eigenvectors in the quotient space of weakly holomorphic modular forms modulo a certain subspace, and it is shown in this paper that the subspace which is factored out is precisely the subspace that is orthogonal to all weakly holomorphic modular forms under an appropriate (regularize) inner product

Regularized inner products and weakly holomorphic Hecke eigenforms

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