Memoirs of the American Mathematical Society 2005; 85 pp; softcover Volume: 178 ISBN10: 0821838768 ISBN13: 9780821838761 List Price: US$61 Individual Members: US$36.60 Institutional Members: US$48.80 Order Code: MEMO/178/841
 The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasiordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local DenefLoeser motivic zeta function \(Z_{\text{DL}}(h,T)\) of a quasiordinary power series \(h\) of arbitrary dimension over an algebraically closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities. This allows us to effectively represent \(Z_{\text{DL}}(h,T)=P(T)/Q(T)\) such that almost all the candidate poles given by \(Q(T)\) are poles. Anyway, these candidate poles give eigenvalues of the monodromy action on the complex \(R\psi_h\) of nearby cycles on \(h^{1}(0).\) In particular we prove in this case the monodromy conjecture made by DenefLoeser for the local motivic zeta function and the local topological zeta function. As a consequence, if \(h\) is a quasiordinary polynomial defined over a number field we prove the Igusa monodromy conjecture for its local Igusa zeta function. Readership Graduate students and research mathematicians interested in analysis and number theory. Table of Contents  Introduction
 Motivic integration
 Generating functions and Newton polyhedra
 Quasiordinary power series
 DenefLoeser motivic zeta function under the Newton maps
 Consequences of the main theorems
 Monodromy conjecture for quasiordinary power series
 Bibliography
