The Number of Zeros of Quadratic Forms with Two Terms

In this paper, we will interest in finding the number of zeros of the quadratic forms over finite fields. We will apply the tool for finding the number of rational points of supersingular curves in [6]. We will give some more tools for Artin-Schreier curves related with quadratic form. We will especially interest in the (supersingular) Artin-Schreier curve $y^q-y=x^{q^b+1}-x^{q^a+1}$.