Rankin-Cohen brackets and Serre derivatives as Poincaré series
arXiv:1801.01906 · doi:10.1007/s40993-018-0130-1
Abstract
We give expressions for the Serre derivatives of Eisenstein and Poincaré series as well as their Rankin-Cohen brackets with arbitrary modular forms in terms of the Poincaré averaging construction, and derive several identities for the Ramanujan tau function as applications.
11 pages