On the Rankin-Selberg problem: higher power moments of the Riesz mean error term

Let ${\mathrm{\Delta }}_1(x;\varphi )$ be the error term of the first Riesz means of the Rankin-Selberg zeta function. We study the higher power moments of ${\mathrm{\Delta }}_1(x;\varphi )$ and derive an asymptotic formula for 3-rd, 4-th and 5-th power moments by using Ivi'c 's large value arguments.