Rankin-Cohen brackets and Serre derivatives as Poincar\'e series
classification
🧮 math.NT
keywords
poincarbracketsderivativesrankin-cohenseriesserreapplicationsarbitrary
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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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