2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96377Let K be a p-adic field. We explore Igusa's p-adic zeta function, which is associated to a K-analytic function on an open and compact subset of K^n. First we deduce a formula for an important coefficient in the Laurent series of this meromorphic function at a candidate pole. Afterwards we use this formula to determine all values less than -1/2 for n=2 and less than -1 for n=3 which occur as the real part of a pole.27 pagesNumber TheoryAlgebraic Geometry11D79; 11S80; 14B05; 14E15text