On the exponential sums estimates related to Fourier coefficients of GL3 Hecke-Maaß forms

Let F be a normlized Hecke-Maass form for the congruent subgroup Gamma 0(N) with trivial nebentypus. In this paper, we study the problem of the level aspect estimates for the exponential sum XLF(alpha) = n <= X AF(n, 1)e(n alpha). As a result, we present an explicit non-trivial bound for the sum LF(alpha) in the case of N = P. In addition, we investigate the magnitude for the non-linear exponential sums with the level being explicitly determined from the sup-norm's point of view as well.