The number of solutions of diagonal cubic equations over finite fields

Let Fq be a finite field of q=pk elements. For any z∈Fq, let An(z) and Bn(z) denote the number solutions equations x13+x23+⋯+xn3=z x13+x23+⋯+xn3+zxn+13=0 respectively. Recently, using generator Fq⁎, Hong Zhu gave generating functions ∑n=1∞An(z)xn ∑n=1∞Bn(z)xn. In this paper, we give ∑n=1∞Bn(z)xn immediately by coefficient z. Moreover, formulas equation a1x13+a2x23+a3x33=0 our are determined coefficients a1,a2 a3. These extend improve earlier results.