The motivic Igusa zeta series of some hypersurfaces non-degenerated with respect to their Newton polyhedron - Schoutens, Hans (Annales Mathematicae Silesianae, 2016)
We describe some algorithms, without using resolution of singularities, that establish the rationality of the motivic Igusa zeta series of certain hypersurfaces that are non-degenerated with respect to their Newton polyhedron. This includes, in any characteristic, the motivic rationality for polydiagonal hypersurfaces, vertex singularities, binomial hypersurfaces, and Du Val singularities.