关于有限域上的本原多项式的系数(英文)

On the Coefficients of Primitive Polynomials Over Finite Fields

证明了对任意给定正整数n和k ,如果满足k <p ,k <n2 且q充分大 ,则在有限域Fg 上存在次数为n的前k个系数预先指定的本原多项式 特别地 ,当k =3 ,4时 。

The author provd the existence of primitive polynomials of degree n with the first k prescribed coefficients over the finite field F q for any given n and k,if k<p, k<n/2, and q larges enough. Particularly, the author gave more specific results if k=3,4.