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
$ \mathscr{L}_F(\alpha) = \sum\limits_{n\le X} A_F(n, 1)e(n \alpha). $
As a result, we present an explicit non-trivial bound for the sum $ \mathscr{L}_F(\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.
Citation: Fei Hou. On the exponential sums estimates related to Fourier coefficients of $ GL_3 $ Hecke-Maaß forms[J]. AIMS Mathematics, 2023, 8(4): 7806-7816. doi: 10.3934/math.2023392
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
$ \mathscr{L}_F(\alpha) = \sum\limits_{n\le X} A_F(n, 1)e(n \alpha). $
As a result, we present an explicit non-trivial bound for the sum $ \mathscr{L}_F(\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.
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Fei Hou. On the exponential sums estimates related to Fourier coefficients of $ GL_3 $ Hecke-Maaß forms[J]. AIMS Mathematics, 2023, 8(4): 7806-7816. doi: 10.3934/math.2023392
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