Young's geodesic QUE conjecture for restricted eigenfunctions

Let $u_j$ be even Hecke–Maass forms normalized by the paper's $L^2$ normalization, and let $f$ be an $L^2$-normalized holomorphic Hecke cusp form of weight $k$. If $\psi:\mathbb{R}^+\to\mathbb{R}$ is smooth and compactly supported, Young's geodesic QUE conjecture.

$$\lim_{j\to\infty}\int_0^\infty|u_j(iy)|^2\psi(y)\frac{dy}{y}=\int_0^\infty2\psi(y)\frac{dy}{y},$$

and

$$\lim_{k\to\infty}\int_0^\infty y^k|f(iy)|^2\psi(y)\frac{dy}{y}=\int_0^\infty\psi(y)\frac{dy}{y}.$$

The conjecture concerns equidistribution after restriction to the vertical geodesic joining $0$ and $i\infty$. The paper proves the analogous statement for Eisenstein series, whereas the corresponding cusp-form assertions are presented as conjectural.