Let $ f(z) $ be a holomorphic Hecke eigenform of weight $ k $ with respect to the full modular group $ SL(2, Z) $, and let $ \Delta_{\rho}(x; sym^{2}f) $ be the error term of the Riesz mean of the symmetric square $ L $-function $ L(s, sym^{2}f) $. In this paper, using a Voronoï type formula for $ \Delta_{\rho}(x; sym^{2}f) $, we consider the third-power moment of $ \Delta_{\rho}(x; sym^{2}f) $ and derive the asymptotic formula for
$ \int_{1}^{T}\Delta_{\rho}^{3}(x;sym^{2}f)dx. $
Citation: Rui Zhang, Xiaofei Yan. The third-power moment of the Riesz mean error term of symmetric square $ L $-function[J]. AIMS Mathematics, 2021, 6(9): 9436-9445. doi: 10.3934/math.2021548
Let $ f(z) $ be a holomorphic Hecke eigenform of weight $ k $ with respect to the full modular group $ SL(2, Z) $, and let $ \Delta_{\rho}(x; sym^{2}f) $ be the error term of the Riesz mean of the symmetric square $ L $-function $ L(s, sym^{2}f) $. In this paper, using a Voronoï type formula for $ \Delta_{\rho}(x; sym^{2}f) $, we consider the third-power moment of $ \Delta_{\rho}(x; sym^{2}f) $ and derive the asymptotic formula for
$ \int_{1}^{T}\Delta_{\rho}^{3}(x;sym^{2}f)dx. $
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Rui Zhang, Xiaofei Yan. The third-power moment of the Riesz mean error term of symmetric square $ L $-function[J]. AIMS Mathematics, 2021, 6(9): 9436-9445. doi: 10.3934/math.2021548
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