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}
}
Comments
11 pages