Sums of Fourier coefficients of certain Eisenstein series of GL(5)

Abstract

Let \(f\) be a Hecke-Maass cusp form for \(\mathrm{SL}_2(\mathbb{Z})\) with normalized Fourier coefficients \(\lambda_f(n)\) and Laplace eigenvalue \(1/4+\mu_f^2\). Let \(g\) be a Hecke-Maass cusp form for \(\mathrm{SL}_2(\mathbb{Z})\) with normalized Fourier coefficients \(\lambda_g(n)\). In this paper, we study the asymptotic of \(\sum_{n \leq X}\lambda_{1\boxplus(f\times g)}(n)\) and get the explicit dependence of the error term on the spectral parameter \(\mu_f\).