A note on the Fourier coefficients of Hecke–Maass forms

To a Hecke–Maass form f(z)f(z) with Laplace eigenvalue 1/4+ν21/4+ν2, we have an automorphic L  -function L(s,sym2f) which is called the symmetric square L-function associated to f  . Suppose that λsym2f(n)λsym2f(n) is the n  th Fourier coefficient of L(s,sym2f). In this paper, the estimate∑n⩽xλsym2f(n)≪ν3/4+εx1/2+ε+x3964+ε is established.