Let $\mathcal{ A}(n)$ be the $(1,n)-th$ Fourier coefficients of $SL(3,\mathbb{ Z})$ Hecke-Maass cusp form i.e. $\Lambda(1,n)$ or the triple divisor function $d_3(n)$, which is the number of solutions of the equation $r_1r_2r_3 = n$ with $r_1, r_2, r_3 \in \mathbb{ Z}^+.$ We establish estimates for \begin{ equation*} \sum_{ 1 \leq n_1,n_2\leq X} \mathcal{ A}(Q(n_1,n_2)) \end{ equation*} where $Q(x,y) \in \mathbb{ Z}[x,y]$ is a symmetric positive definite quadratic form.
Categories: math.NT