A spectral mean value theorem for \(\text{GL}(3)\) (Q710480)

Let \(\{\phi_j\}\) be an orthonormal basis of Maaß forms for \(\text{SL}(3,{\mathbb Z})\), and \(W_j^{(1,1)}(y)\) be the first Fourier coefficient of \(\phi_j\). The paper gives a bound on the averages of \(|W_j^{(1,1)}(y)|^2\) over certain subsets of the cuspidal spectrum of \(\text{SL}(3)\), when \(y\) is a fixed diagonal matrix that is sufficiently dominant. The proof is an elegant application of Kuznetsov formula in \(\text{SL}(3)\) case, which is much more complex than the formula in \(\text{SL}(2)\) case.