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带有尖形式Fourier系数的指数和估计
The Exponential Sum Related to the Fourier Coefficient of Cusp Form
设λf（n）是全模群Γ上权为k的全纯Hecke特征形f的第n个Fourier系数，Λ（n）是Mangoldt 函数. 本文得到了如下估计 ΣX<n≤2XΛ（n）λf（n）e（√nα）<<f，α X（5/6）（logX）（13/2），（α>0），改进了Zhao的结果.
Let λf(n) be the n-th Fourier coefficient of a holomorphic Hecke eigenform f of weight k for the full modular group Γ, Λ(n) is the Mangoldt function. In this paper, we proved the following result:ΣX<n ≤ 2XΛ(n)λf(n)e(√nα)<<f,α X(5/6)(logX)(13/2),(α>0), which improved Zhao's result.
尖形式 / 指数和 / Rankin-Selberg L-函数 {{custom_keyword}} /
cusp form / exponential sum / Rankin-Selberg L-function {{custom_keyword}} /
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国家自然科学基金资助项目（11371122，11471112）；2011河南省创新型科技人才队伍建设工程，2013年河南省科技创新杰出人才河南省科技攻关项目（152102310320），河南省教育厅重点科研项目（17A110009）
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