Differential operators on modular forms associated to quasimodular forms.

A quasimodular form $$\phi $$ of depth at most $$m$$ corresponds to holomorphic functions $$\phi _0, \phi _1, \ldots , \phi _m$$ . Given nonnegative integers $$\alpha $$ and $$\nu $$ with $$\nu \le m$$ , we introduce a linear differential operator $$\mathcal D_{\phi }^{\alpha , \nu }$$ of order $$\nu $$ on modular forms whose coefficients are given in terms of derivatives of the functions $$\phi _k$$ . We then show that Rankin-Cohen brackets of modular forms can be expressed in terms of such operators. As an application, we obtain differential operators associated to certain theta series studied by Dong and Mason. [ABSTRACT FROM AUTHOR]