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Let $f$ be a nearly holomorphic modular form on a Hilbert modular variety $Sh$. Suppose that $f$ vanishes on a Zariski dense subset of CM points on $Sh$. How to show that $f$ is identically zero?

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  • $\begingroup$ This is an interesting question even for $GL_2 / \mathbf{Q}$ (where nearly holomorphic modular forms are just polynomials in $E_2$ with coefficients that are modular forms). $\endgroup$ Nov 23, 2015 at 8:03

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