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

TL;DR

This paper investigates the higher power moments of the error term in the Riesz means of the Rankin-Selberg zeta function, providing asymptotic formulas for the third, fourth, and fifth moments using advanced large value techniques.

Contribution

It introduces new asymptotic formulas for higher power moments of the error term in the Riesz means, extending previous understanding of its distribution.

Findings

Derived asymptotic formulas for 3rd, 4th, and 5th power moments

Applied Ivić's large value arguments to the error term analysis

Enhanced understanding of the distribution of the error term in Rankin-Selberg zeta functions

Abstract

Let $\Delta_1(x;\phi)$ be the error term of the first Riesz means of the Rankin-Selberg zeta function. We study the higher power moments of $\Delta_1(x;\phi)$ and derive an asymptotic formula for 3-rd, 4-th and 5-th power moments by using Ivi\'c 's large value arguments.