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arXiv · 1801.01906

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

Brandon Williams
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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.

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Brandon Williams. 2018-01-05. Rankin-Cohen brackets and Serre derivatives as Poincar\'e series. https://doi.org/10.1007/s40993-018-0130-1

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