an:05896164 Zbl 1214.14004 Artal Bartolo, E.; Cassou-Nogu\`es, Pi; Luengo, I.; Melle Hern\'andez, A. On $\nu$-quasi-ordinary power series: factorization, Newton trees and resultants. EN Cogolludo-Agust{\'\i}n, Jos\'e Ignacio (ed.) et al., Topology of algebraic varieties and singularities. Invited papers of the conference in honor of Anatoly Libgober's 60th birthday, Jaca, Spain, June 22--26, 2009. Providence, RI: American Mathematical Society (AMS); Madrid: Real Sociedad Matem\'atica Espa\~nola. Contemporary Mathematics 538, 321-343 (2011). ISBN 978-0-8218-4890-6/pbk 2011

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*14B05 32S05 32S10 quasi-ordinary power series; resultant; factorization Summary: A generalization of quasi-ordinary power series is studied. This class, called $\nu$-quasi-ordinary, was introduced by H. Hironaka and it is defined by a very mild condition on its (projected) Newton polygon. I. Luengo used $\nu$-quasiordinary power series to give a proof of the Jung-Abhyankar theorem for quasiordinary power series. In this paper, a factorization theorem for $\nu$-quasi-ordinary power series is given. Using the factorizacion theorem we codify $\nu$-quasiordinary power series by its Newton tree, and we use it to compute the generalized intersection multiplicity of two $\nu$-quasiordinary power series, resultant and discriminant.