Average behaviour of higher moments of cusp form coefficients

Abstract

Let $f$ be a primitive holomorphic cusp form of even integral weight for the full modular group $\Gamma=SL(2,\mathbb{Z})$. In this paper, we study the higher moments of general divisor problem related to the coefficients of Rankin-Selberg $L$-function $L(f\times f,s)$ associated with $f$ over sum of two squares.