2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71546In 1987, C. Sabbah proved the existence of Bernstein-Sato polynomials associated with several analytic functions. The purpose of this article is to give a more elementary and constructive proof of the result of C. Sabbah based on the notion of the analytic Gröbner fan of a D-module.17 pages, 4 figures. This is a translation into english of the accepted version of math.RA/0307179 which is to appear in Compositio MathRings and Algebrastext