On the higher moments of the error term in the Rankin-Selberg problem

Let ${\mathrm{\Delta }}_1(x;\phi )$ denote the error term in the classical Rankin-Selberg problem. In this paper, we consider the higher power moments of ${\mathrm{\Delta }}_1(x;\phi )$ and derive the asymptotic formulas for 3-rd, 4-th and 5-th power moments, which improve the previous results.