On the number of zeros of diagonal cubic forms

Let Ms, be the number of solutions of the equation X13+ X23+ … + Xs3=0 in the finite field GF(p). For a prime p ≡ 1(mod 3), ∑∞s=1 MsX3 = (x/1-px)+((x2(p-1)(2+dx))/(1-3px2-pdx3)), M3= p2 + d(p - 1), and M4 = p2 + 6(p2 − p). Here d is uniquely determined by 4p = d2 + 27b2 and d ≡ 1(mod 3)