Harmonic lifts of modular forms

Abstract

It is shown that each complex conjugate of a meromorphic modular form for ${\mathrm{SL}}_2(\mathbb{Z})$ of any complex weight $p$ occurs as the image of a harmonic modular form under the operator $2i{y}^p{\partial }_{\bar{z}}$. These harmonic lifts occur in holomorphic families with the weight as the parameter.

References in corpus (1)

• On a completed generating function of locally harmonic Maass forms

Cited by in corpus (1)

• Weak Maass-Poincare series and weight 3/2 mock modular forms