On Rankin-Cohen Brackets of Hecke Eigenforms and Modular Forms of Half-Integral Weight

2024/05/27 by Choie, YoungJu, Kohnen, Winfried, Zhang, Yichao
#11F11 #11F25 #11F37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2405.16745

Abstract

We generalize the linear relation formula between the square of normalized Hecke eigenforms of weight k and normalized Hecke eigenforms of weight 2k, to Rankin-Cohen brackets of general degree. As an ingredient of the proof, we also generalize a formula of Zagier on the Petersson inner product of Rankin-Cohen brackets involving Eisenstein series.

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• Dirichlet series of Rankin-Cohen Brackets
• Rankin-Cohen Brackets of Hilbert Hecke Eigenforms
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• On The Hecke Eigenforms of Half-Integral Weight and Dedekind-Eta Products