Witt Expansion Of The Function Domain Zeta Function Calculation

In this paper, we study the special Witt extension tower of a function field and the computation of it's zeta function. Let p be a fixed prime number, Fp the finite field of p elements. Let x be a transcendentalelement over Fp, X = (x,0,....,0) an element in the ring of Witt vectors Wm(Fp(x)) . Denote by Fp(x)(y0,y1,.......y(m-1)) function field extension over Fp(x) by joining yI,0