General divisor problem pertaining to the $l$-fold product $L$-function over sum of four squares

In this paper, we study a general divisor problem associated with the $l$-fold product $L$-function. More precisely, we establish the general asymptotic formulas for the higher moments of Hecke eigenvalues of general product $L$-function over the sequence of natural numbers and over a special subsequence of natural numbers, namely the sum of four squares.