English

On Rankin-Cohen Brackets of Hecke Eigenforms and Modular Forms of Half-Integral Weight

Number Theory 2024-05-28 v1

Abstract

We generalize the linear relation formula between the square of normalized Hecke eigenforms of weight kk and normalized Hecke eigenforms of weight 2k2k, to Rankin-Cohen brackets of general degree. As an ingredient of the proof, we also generalize a formula of Zagier on the Petersson inner product of Rankin-Cohen brackets involving Eisenstein series.

Keywords

Cite

@article{arxiv.2405.16745,
  title  = {On Rankin-Cohen Brackets of Hecke Eigenforms and Modular Forms of Half-Integral Weight},
  author = {YoungJu Choie and Winfried Kohnen and Yichao Zhang},
  journal= {arXiv preprint arXiv:2405.16745},
  year   = {2024}
}