English

Harmonic lifts of modular forms

Number Theory 2012-06-25 v1

Abstract

It is shown that each complex conjugate of a meromorphic modular form for SL2(Z)\mathrm{SL}_2(\mathbb{Z}) of any complex weight pp occurs as the image of a harmonic modular form under the operator 2iypzˉ2i y^p \, \partial_{\bar z}. These harmonic lifts occur in holomorphic families with the weight as the parameter.

Keywords

Cite

@article{arxiv.1206.5118,
  title  = {Harmonic lifts of modular forms},
  author = {Roelof W. Bruggeman},
  journal= {arXiv preprint arXiv:1206.5118},
  year   = {2012}
}
R2 v1 2026-06-21T21:23:50.419Z