Newton polygons of L-functions of polynomials of the form Xd+λX

Let f(x)=xd+λx be a polynomial over Fq. The purpose of this paper is to determine the Newton polygon for the L-function L(f,T) of exponential sums attached to the one variable polynomial f(x) over a finite field of characteristic p. The first slope of the Newton polygon is calculated for all equivalence classes of d. The entire Newton polygon is given for when p≡−1 mod d.