TITLE: The sixth power integral moment of automorphic L-function attached to Maass Forms
QUESTION [5 upvotes]: It is known that the sixth power integral moment of  automorphic L-function attached to Cusp Forms has been proved by M. Jutila, that is $\int_{0}^{T}|L(1/2+it,f)|^{6}dt \ll T^{2+\varepsilon}$.
 And it should also be true for Maass Forms philosophically, are there some references about this?

REPLY [3 votes]: I have seen several papers in this direction, but don't know exactly what is known. Perhaps the following reference is helpful:
M. P. Young obtains in his article The second moment of $GL(3)\times GL(2)$ L-functions at special points in $2009$ such estimates for a family of $L$-functions $L(φ×u_j,s)$ where $u_j$ runs over the family of Hecke-Maass cusp forms on $SL(2,\mathbb{Z})$, $\phi$ is a fixed $SL(3,\mathbb{Z})$ Maass form (Rankin-Selberg convolution of $\phi$ with $u_j$)
; at the special points $\frac{1}{2}+it_j$. The results are stated in Theorems $3.1$ and $3.2$. In particular,
$$
\sum_{t_j\le T}|L(u_j, \frac{1}{2}+it_j|^6 \ll T^{2+\varepsilon}.
$$