On a conjecture of Wan about limiting Newton polygons

Yi Ouyang; Jinbang Yang

On a conjecture of Wan about limiting Newton polygons

Number Theory 2015-10-28 v1

Authors: Yi Ouyang , Jinbang Yang

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 $f\mod\mathfrak p$ does not converge for $\mathfrak p$ 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.

Keywords

limiting Newton polygons Newton polygon convergence global permutation polynomial monic polynomial number field finite places Wan's conjecture

Cite

@article{arxiv.1510.07772,
  title  = {On a conjecture of Wan about limiting Newton polygons},
  author = {Yi Ouyang and Jinbang Yang},
  journal= {arXiv preprint arXiv:1510.07772},
  year   = {2015}
}

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