Equations involving the modular $j$-function and its derivatives

Vahagn Aslanyan, Sebastian Eterović, Vincenzo Mantova

We show that for any polynomial $F(X,Y_0,Y_1,Y_2)\in \mathbb{C}[X,Y_0,Y_1,Y_2]$, the equation $F(z,j(z),j^{\prime }(z),j^{\prime \prime }(z))=0$ has a Zariski dense set of solutions in the hypersurfac…