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In this paper, we shall precise the asymptotic behaviour of Newton polygonsof $L$ functions associated to character sums, coming from some $n$ variableLaurent polynomials. In order to do this, we use the free sum on convexpolytopes. This operation allows the determination of the limit of genericNewton polygons for the sum $\Delta=\Delta_1\oplus \Delta_2$ when we know thelimit of generic Newton polygons for each factor. To our knowledge, these arethe first results concerning the asymptotic behaviour of Newton polygons formultivariable polynomials.

Polygones de Newton de certaines sommes de caract\`eres et s\'eries de Poincar\'e