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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.

MSC:
 11F11 Holomorphic modular forms of integral weight 11F12 Automorphic forms, one variable
Keywords:
modular forms; Rankin-Cohen brackets
Full Text:
References:
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