2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111510Principal value integrals are associated to multi-valued rational differential forms with normal crossings support on a non-singular algebraic variety. We prove their vanishing on rational surfaces in the context of a conjecture of Denef-Jacobs. As an application we obtain a strong vanishing result for candidate poles of p-adic and motivic Igusa zeta functions.20 pages, to appear in J. Reine Angew. MathAlgebraic Geometry14J26 (11S80; 14E15; 28B99; 14F17)text