BCG conjecture

Let $K$ be a complex cubic field, let $\mathfrak f$ be a conductor ideal, let $c$ be a ray class group element, let $\mathfrak s$ be a smoothing ideal, and let $L$ be the relevant lattice. If $Q_{\mathfrak f,c,\mathfrak s}(h)$ denotes the corresponding smoothed quotient of elliptic Gamma values at a torsion point $h$, then the conjecture asserts that $Q_{\mathfrak f,c,\mathfrak s}(h)$ depends only on the class of $h$ modulo $L$: for every admissible torsion point $h$ and every $\ell\in L$, $Q_{\mathfrak f,c,\mathfrak s}(h+\ell)=Q_{\mathfrak f,c,\mathfrak s}(h)$ whenever both sides are defined.