‘CM class field’ of the reflex field $\tilde K$, and let $L_K=M H_{\tilde K}$. Then $M(\tilde\Psi_1(z), \tilde\Psi_2(z))$ is a subfield of $L_K$ with bounded index $[L_K:M(\tilde\Psi_1(z),
    \tilde\Psi_2(z))] \le d$.

3.  One has $\lim_{q \rightarrow \infty} \frac{\log
    [M(\tilde\Psi_1(z), \tilde\Psi_2(z)): M]}{\log  \sqrt q}=1$.

In [@BY] the authors derived a formula for the values of (untwisted) Borcherds products (in the sense of [@BB]) at CM cycles ${\mathcal{CM}}(K)$. It would be very interesting to obtain an analogous formula for the CM values of the twisted Borcherds products of Theorem \[hilbertintro\]. In fact one can ask if it is possible to modify the proof of [@BY] to give such a result. One key ingredient of the proof – the relation between Borcherds products and automorphic Green functions – is already worked out in the present paper. However, in the second main step of the argument it is not clear at all how the function $\psi$ on the lattice $L^0$ defined in translates to some natural function on the reflex field $\tilde K$. In Section \[sect:examples\] we study some examples in the special case that $F={\mathbb{Q}}(\sqrt{5})$. We write $\tilde \Psi_1$ and $\tilde \Psi_2$ in terms of the generators of the ring of symmetric Hilbert modular forms 