Sum of the GL(3) Fourier coefficients over mixed powers

Let S(n) be the (1,n)th Fourier coefficient of SL(3, Z) Hecke-Maass cusp form, denoted as A(1,n) or the triple divisor function, denoted as d(3)(n). Let k >= 3 be an integer. In this paper, we establish an asymptotic formula for the sum Sigma(1,n2 <= X)1(/2) (1 <= n3 <= X)1(/k) A(Q(n(1),n(2))+n(3)(k))a(n (3)), where a(n) is either von Mangoldt function or identity function, and Q(x,y) is an element of Z[x,y] is a binary quadratic polynomial. When A(n) = A(1,n), then a(n) can be any bounded arithmetical function.