摘要
设q为一个正整数,f(x)=sum from n=0 to ka_nx^n(k≥4)是一个适合条件(a_1,a_2,…,a_k)=1,且(na_n,q)=(1<n<k)的整系数多项式,f′(x)=sum from n=1 to kna_nx^(n-1),f″(x)=sum from n=2 to kn(n-1)a_nx^(n-2),s(q,f(x))=tom from x=1 e^(2πif(x)/a),那未在条件f′(x)≡0,f″(x)≡0(modp)无公解下,本文证明了,对于素数p和整数1>l有|s(p^1,f(x)|≤(k-1)p^V,其中 1/2,1=1或偶数 V= ,以及对任意 (1+1)/2,1≥3且1为奇数自然数a有 |s(a,f(x))|≤e(0.247(k-1)~4)q(3/4)
Suppose that q is a positive integer and f(x)=sum from n=0 to k(a_лx~л)(k≥4) is an integral a_2,…,a_k)=1 and(na_л,q coeffictents plynomial that satisfies conditions (a_1, a_2, …, a_k ) =1 and(na_n, q) =1 (1≤n≤k), S(q, f(x))=sum from x=1 to q(e^(2πif(x)/q)), Under the conditions of f'(x)≡0 and f''(x)≡0 (modp) have no public solves, we proved |S(p^l, f(x))|≤(k-1)p^v, v=l/2 l=1 or even number, (l+1)/2 l≥3 an odd number. for prime number p and inteqer l>1 and |S(q, f(x))|≤e^(0.247(k-1)~4) q^(3/4) for every natural number.
出处
《陕西科技大学学报（自然科学版）》
1992年第1期93-104,共12页
Journal of Shaanxi University of Science & Technology
