We construct a solution T0 in the distribution sense of equation fT = 1 near a critical point of f and we give an upper bound for the order of T0 in terms of f's Newton Polyhedron, provided f is non degenerate in some sense. The order of T0 is equal to this upper bound when f is non-negative.
@article{urn:eudml:doc:41514, title = {Sur l'ordre de la distribution 1/f.}, journal = {Publicacions Matem\`atiques}, volume = {37}, year = {1993}, pages = {3-17}, mrnumber = {MR1240919}, zbl = {0808.46049}, language = {fr}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41514} }
Diallo, Seydou Nourou; Sargos, Patrick. Sur l'ordre de la distribution 1/f.. Publicacions Matemàtiques, Tome 37 (1993) pp. 3-17. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41514/