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Notes on Rankin-Cohen brackets. (English) Zbl 1244.11039
Summary: The Rankin-Cohen product of two modular forms is known to be a modular form. The same formula can be used to define the Rankin-Cohen product of two holomorphic functions \(f\) and \(g\) on the upper half-plane. Assuming that this product is a modular form, we prove that both \(f\) and \(g\) are modular forms if one of them is. We interpret this result in terms of solutions of linear ordinary differential equations.

11F11 Holomorphic modular forms of integral weight
11F12 Automorphic forms, one variable
Full Text: DOI
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