Rankin-Cohen brackets and Serre derivatives as Poincaré series

Published 5 Jan 2018 in math.NT | (1801.01906v2)

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

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