  For the shifted convolution sum $$
D_h(X)=\sum_{m=1}^\infty\lambda_1(1,m)\lambda_2(m+h)V(\frac{m}{X}) $$ where
$\lambda_1(1,m)$ are the Fourier coefficients of a $SL(3,\mathbb Z)$ Maass form
$\pi_1$, and $\lambda_2(m)$ are those of a $SL(2,\mathbb Z)$ Maass or
holomorphic form $\pi_2$, and $1\leq |h| \ll X^{1+\varepsilon}$, we establish
the bound $$ D_h(X)\ll_{\pi_1,\pi_2,\varepsilon} X^{1-(1/20)+\varepsilon}. $$
The bound is uniform with respect to the shift $h$.
