Yui and Zagier made some fascinating conjectures on the factorization on the norm of the difference of Weber class invariants $ f(\mathfrak a_1) - f(\mathfrak a_2)$ based on their calculation in \cite{ YZ}. Here $\mathfrak a_i$ belong two diferent ideal classes of discrimants $D_i$ in imagainary quadratic fields $\mathbb{ Q}(\sqrt{ D_i})$. In \cite{ LY}, we proved these conjectures and their generalizations when $(D_1, D_2) =1$ using the so-called big CM value formula of Borcherds lifting. In this sequel, we prove the conjectures when $\mathbb{ Q}(\sqrt{ D_1}) =\mathbb{ Q}(\sqrt{ D_2})$ using the so-called small CM value formula. In addition, we give a precise factorization formula for the resultant of two different Weber class invariant polynomials for distinct orders.
Categories: math.NT