Subconvexity conjecture for the Rankin–Selberg convolution of Siegel cusp forms

Let $F$ be a Siegel cusp form of weight $k$, and let $R(s,F,F)$ denote its Rankin–Selberg convolution. The critical line is

$$\operatorname{Re}(s)=k-\frac{n+1}{4}.$$

Subconvexity conjecture. There exists $\delta>0$ such that

$$R\left(k-\frac{n+1}{4}+it,F,F\right)\ll_{t,n}\left(\operatorname{Res}_{s=k}R(s,F,F)\right)k^{\frac{n(n+1)}4-\delta}.$$

This would improve the convexity bound by a power of $k$ and is the subconvexity estimate needed for the paper's analysis of Rankin–Selberg convolutions.