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λ_f/(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∑_(X<n≤2X)Λ(n)λ_f(n)e(n^(1/2)α)■f,αX^(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 Г, ∧（n） is the Mangoldt function. In this paper, we proved the following result：∑x〈n≤2x∧（n）λf（n）e（√na）〈〈f,aX 56（log,X）13/2,（a〉0）which improved Zhao＇s result.