Let α be a real number, x≥A≥2, e(θ) = e^(2xiθ), and suppose Λ(n) is Mangoldt's func-tion. In this paper the following result is mainly proved: Let ε be an arbitrarily small po-sitive number, and x^(91/(96+...Let α be a real number, x≥A≥2, e(θ) = e^(2xiθ), and suppose Λ(n) is Mangoldt's func-tion. In this paper the following result is mainly proved: Let ε be an arbitrarily small po-sitive number, and x^(91/(96+ε))≤A≤x. Then for any given positive c, there exists a positive c_1such that for A^(-1)log^cx ≤|α| ≤(logx)^(-c_1) there exitss sum from x-A<n≤x (Λ(n)e(nα)? A(logx)^(-c).展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Let α be a real number, x≥A≥2, e(θ) = e^(2xiθ), and suppose Λ(n) is Mangoldt's func-tion. In this paper the following result is mainly proved: Let ε be an arbitrarily small po-sitive number, and x^(91/(96+ε))≤A≤x. Then for any given positive c, there exists a positive c_1such that for A^(-1)log^cx ≤|α| ≤(logx)^(-c_1) there exitss sum from x-A<n≤x (Λ(n)e(nα)? A(logx)^(-c).
