Newton polygons of L functions of polynomials xd + ax

Let p   be a prime number and q=phq=ph. For f(x)=xd+ax∈Fq[x](a≠0), we obtain the slopes of the Newton polygons of the L  -functions of the exponential sums associated to f(x)f(x) for any nontrivial finite character χ. For χ of order p, our result recovers Zhu's genericity result [10] by giving p an explicit bound. The general χ case is based on improvement of results of Davis–Wan–Xiao [2].