Polygones de Newton de certaines sommes de caractères et séries de Poincaré

Details Polygones de Newton de certaines sommes de caractères et séries de Poincaré Polygones de Newton de certaines sommes de caractères et séries de Poincaré

2008-02-26

arxiv.org/abs/0802.3889v1

Mathematics

Number Theory

22 pages, french

Scientific paper

In this paper, we shall precise the asymptotic behaviour of Newton polygons of $L$ functions associated to character sums, coming from some $n$ 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 $\Delta=\Delta_1\oplus \Delta_2$ when we know the limit of generic Newton polygons for each factor. To our knowledge, these are the first results concerning the asymptotic behaviour of Newton polygons for multivariable polynomials.

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