Éditeur(s) : HAL CCSD
Résumé : accepté pour publication par l'International Journal of Number Theory
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 $Delta=Delta_1oplus Delta_2$ 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 when the generic Newton polygon differs from the combinatorial (Hodge) polygon associated to the polyhedron.
https://hal.archives-ouvertes.fr/hal-00551461

Droits : info:eu-repo/semantics/OpenAccess
hal-00551461
https://hal.archives-ouvertes.fr/hal-00551461
https://hal.archives-ouvertes.fr/hal-00551461/document
https://hal.archives-ouvertes.fr/hal-00551461/file/prodpolytopespubli.pdf