有限域上的二次型表数

The Number of Quadratic Forms Representations in Finite Fields

令Fq为有限域,其中q=pt,p为奇素数,t为正整数.设f(x1,…,xn)为Fq上的n元二次型,α∈Fq,本文给出方程f(x1,…,xn)=α在Fq上的非零解数的具体公式.

Let q =p＇,where p is an odd prime number and t is a positive integer. Let Fq be a finite field with q elements. In this note, for any α∈Fq, we give a formula of the number of nonzero representations of α by a quadratic form f（ x1,…,xn.）in Fq,.