关于不完整三角和的估计

On Estimate of Non-Complete Trigonometric Sun

本文改进了华罗庚关于不完整三角和的著名结果,我们主要证明了: |sum from x=1 to m eq(f(x))-m/q S(q,f)x))| <4/x^2(logq+βπ+3/4-logπ/2)e^(2k)q^(1-1/k)+2/π(2-1π)e^(2k)q^(-1/k)。其中f(x)=a_kx^k+……+a_1x+a_0为一整系数多项式,且(a_1,a_2……a_k,q)=1,γ为Enler常数,q≥2整数。

Author improved a famous result of Hua Lougin's Non-Complete Trigonometric sun, main proved:|sum from x=1 to m eq(f(x))-m/q S(q,f(x))|<7/x^2(logq+γπ+3/4-logπ/2)e^(2k)q^(1-1/k)+2/π(2-1/π)e^(2k)q^(-1/k). In our result, f(x)=α_kx^k+……+α_1x+α_0 is a complete ordinal number polynomial, ang (α_1,α_2……α_k,q)=1,γ is Enter constant, q≥2 integer.