English

Rankin-Cohen brackets and Serre derivatives as Poincar\'e series

Number Theory 2018-09-28 v2

Abstract

We give expressions for the Serre derivatives of Eisenstein and Poincar\'e series as well as their Rankin-Cohen brackets with arbitrary modular forms in terms of the Poincar\'e averaging construction, and derive several identities for the Ramanujan tau function as applications.

Keywords

Cite

@article{arxiv.1801.01906,
  title  = {Rankin-Cohen brackets and Serre derivatives as Poincar\'e series},
  author = {Brandon Williams},
  journal= {arXiv preprint arXiv:1801.01906},
  year   = {2018}
}

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11 pages