On a conjecture of Wan about limiting Newton polygons

Abstract

We show that for a monic polynomial f (x) over a number field K containing a global permutation polynomial of degree > 1 as its composition factor, the Newton Polygon of f mod p does not converge for p passing through all finite places of K. In the rational number field case, our result is the "only if" part of a conjecture of Wan about limiting Newton polygons.