Some remarks on Rankin-Cohen brackets of eigenforms
Jaban Meher
TL;DR
This paper explores when products and Rankin-Cohen brackets of eigenforms remain eigenforms, extending previous results to more general cases involving quasimodular and nearly holomorphic forms.
Contribution
It generalizes Ghate's results to include Rankin-Cohen brackets of eigenforms, broadening understanding of their eigenform properties.
Findings
Identifies conditions under which products of eigenforms are eigenforms.
Extends previous work to Rankin-Cohen brackets of eigenforms.
Provides new insights into the structure of quasimodular and nearly holomorphic eigenforms.
Abstract
We investigate the cases for which products of two quasimodular or nearly holomorphic eigenforms are eigenforms. We also genaralize the results of Ghate \cite{ghate1} to the case of Rankin-Cohen brackets.
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