We generalize Kronecker’s solution of Pell’s equation to CM fields $K$ whose Galois group over $\mathbb{Q}$ is an elementary abelian 2-group. This is an identity which relates CM values of a certain Hilbert modular function to products of logarithms of fundamental units. When $K$ is imaginary quadratic, these CM values are algebraic numbers related to elliptic units in the Hilbert class field of $K$. Assuming Schanuel’s conjecture, we show that when $K$ has degree greater than 2 over $\mathbb{Q}$ these CM values are transcendental....