Deng–Espinosa's cubic order zeta-function conjecture

Let $R$ be a Gorenstein order over $\mathbb{Z}$. Let $R^\vee=\operatorname{Hom}(R,\mathbb{Z})$, and define Yun's Dedekind zeta function by

$$J_R(s)=\sum_{M\subset R^\vee}[R^\vee:M]^{-s}.$$

Here $L(s,R)$ is the cubic-order $L$-function defined by summing over the overorders of $R$, and $\zeta_{\mathbb{Q}}(s)$ is the Riemann zeta function. Deng–Espinosa's conjecture. One has

$$J_R(s)=L(s,R)\zeta_{\mathbb{Q}}(s).$$

The conjecture proposes that the order zeta function introduced by Yun factors through the explicitly defined cubic-order $L$-function, generalizing the established relationship for $\mathrm{GL}_2(\mathbb{Q})$. Its status is not determined by the supplied source context.