关于完整三角和估计的一点注记(英文)

Let q be an integer, f(x)=a_kx~k+…+a_1x+a_0 be a polynomial withintegral coefficients and (a_1,…,a_k,q)=1. Also set Ss(q,f(x))=sum from x=1 to q e~(2πif(?)lq) (1) In 1940, Hua Loo Keng~(1]) first obtained that S(q,f(x))=O(q~(1-1/k+(?))), (2)where the exponcnt 1-1/k is best possible. Since then many mathematicians have sought to improve the constant implied by O in (2). The best two results were obtained by Chen Jing run~(2] and ~3] in 1977. The result of 2] is