Young's shifted convolution conjecture for Maass forms

Let $U(z)$ be a Hecke–Maass cusp form with Laplace eigenvalue $1/4+T^2$, Fourier coefficients $\lambda(n)$, and first Fourier coefficient $\rho(1)$. For fixed $0<a\le y\le b$, nonzero integer $m$, and some fixed $\tau>0$ and $R\ge0$, Young's shifted convolution conjecture.

$$|\rho(1)|^2\sum_{n\in\mathbb{Z}}\lambda(n)\lambda(n+m)K_{iT}(2\pi|n|y)K_{iT}(2\pi|m+n|y)\ll_{a,b,\tau,R}T^{-\tau+\varepsilon}|m|^R.$$

This is a shifted-convolution estimate designed to imply cancellation in Fourier coefficients of restricted eigenfunctions and hence quantitative QUE or sup-norm bounds. The passage gives no resolution status, so the estimate remains conjectural here.