Arthur's multiplicative formula conjecture for orbital integrals in $\operatorname{GL}(2)$

Let $K=\mathbb{Q}$, let $\gamma$ be a contributing matrix, and let $S_{\gamma}$ and $D_{\gamma}$ be the positive integer and fundamental discriminant associated with $\gamma$ as in Langlands's formula. Put $d'=S_{\gamma}/d$. For each prime $q$, let $\tilde{J}_{\mathbb{Z}_q[\gamma]}(s)$ denote the local factor defined above. Arthur's conjecture. The following equality holds:

$$S_{\gamma}^s\sum_{d\mid S_{\gamma}}d^{1-2s}\prod_{p\mid d'}\left(1-\frac{\left(\frac{D_{\gamma}}{p}\right)}{p^s}\right)=\prod_q\tilde{J}_{\mathbb{Z}_q[\gamma]}(s).$$

This predicts a multiplicative factorization of the complex function arising from Langlands's formula for orbital integrals into local factors indexed by the primes. The supplied text gives no evidence that the conjecture has been proved or disproved.