Integral mean-square estimation of error terms of Fourier coefficients attached to cusp forms.

Let f, g be two distinct primitive holomorphic cusp forms of even integral weights k 1 , k 2 for the full modular group Γ = S L (2 , Z) , respectively. In this paper, we are interested in the upper bounds for the integral mean square of error terms involving λ f 2 i 1 (n) , λ f 2 (n j 1) and λ f 2 (n i 2) λ g 2 (n j 2) on average in terms of f, g respectively. Here i 1 ≥ 2 , j 1 ≥ 3 and i 2 , j 2 ≥ 1 are positive integers. [ABSTRACT FROM AUTHOR]