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.
@article{bwmeta1.element.doi-10_1515_amsil-2016-0010,
author = {Hans Schoutens},
title = {The Motivic Igusa Zeta Series of Some Hypersurfaces Non-Degenerated with Respect to their Newton Polyhedron},
journal = {Annales Mathematicae Silesianae},
volume = {30},
year = {2016},
pages = {143-179},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_amsil-2016-0010}
}
Hans Schoutens. The Motivic Igusa Zeta Series of Some Hypersurfaces Non-Degenerated with Respect to their Newton Polyhedron. Annales Mathematicae Silesianae, Tome 30 (2016) pp. 143-179. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_amsil-2016-0010/