Newton Polygons and Families of Polynomials

Newton polygons for character sums and Poincaré series

In this paper, we precise the asymptotic behaviour of Newton polygons of L-functions associated to character sums, coming from certain n variable Laurent polynomials. In order to do this, we use the free sum on convex polytopes. This operation allows the determination of the limit of generic Newton polygons for the sum ∆ = ∆1 ⊕ ∆2 when we know the limit of generic Newton polygons for each facto...

m at h . N T ] 1 8 Ju n 20 07 NEWTON POLYGONS FOR TWISTED EXPONENTIAL SUMS AND POLYNOMIALS

We study the p-adic absolute value of the roots of the L-functions associated to certain twisted character sums, and additive character sums associated to polynomials P (x d), when P varies among the space of polynomial of fixed degree e over a finite field of characteristic p. For sufficiently large p, we determine in both cases generic Newton polygons for these L-functions, which is a lower b...

Higher Order Bernoulli Polynomials and Newton Polygons

Newton Polygons of Polynomial Ordinary Differential Equations

In this paper we show some properties of the Newton polygon of a polynomial ordinary differential equation. We give the relation between the Newton polygons of a differential polynomial and its partial derivatives. Newton polygons of evaluations of differential polynomials are also described.

Newton Polygons for Twisted Exponential Sums

We study the p-adic absolute value of the roots of the L-functions associated to certain twisted character sums, and additive character sums associated to polynomials P (x d), when P varies among the space of polynomial of fixed degree e over a finite field of characteristic p. For sufficiently large p, we determine in both cases generic Newton polygons for these L-functions, which is a lower b...