Artal Bartolo, EnriqueCassou-Noguès, PierretteLuengo Velasco, IgnacioMelle Hernández, AlejandroCogolludo Agustín, José IgnacioHironaka, Eriko2023-06-202023-06-202011S. Abhyankar, On the rami�cation of algebraic functions, Amer. J. Math. 77 (1955), 575-592. E. Artal, Pi. Cassou-Nogu�es, I. Luengo, and A. Melle Hern�andez, Quasi-ordinary power series and their zeta functions, Mem. Amer. Math. Soc. 178 (2005), no. 841, vi+85. E. Artal, Pi. Cassou-Nogu�es, I. Luengo, and A. Melle Hern�andez, Quasi-ordinary singularities and Newton trees, submitted, 2010. Pi. Cassou-Nogu�es, Algebraic curves, Book in preparation. D. Eisenbud and W.D. Neumann, Three-dimensional link theory and invariants of plane curve singularities, Annals of Mathematics Studies, vol. 110, Princeton University Press, Princeton, NJ, 1985. P. D. Gonz�alez-P�erez, Singularit�es quasi-ordinaires toriques et poly�edre de Newton du dis-criminant, Canad. J. Math. 52 (2000), no. 2, 348-368. P. D. Gonz�alez-P�erez, Toric embedded resolutions of quasi-ordinary hypersurface singularities, Ann. Inst. Fourier (Grenoble) 53 (2003), no. 6, 1819-1881. P. D. Gonz�alez-P�erez, L. J. McEwan, and A. N�emethi, The zeta-function of a quasi-ordinary singularity. II, Topics in algebraic and noncommutative geometry (Luminy/Annapolis, MD, 2001), Contemp. Math.,vol.324,Amer. Math. Soc., Providence, RI, 2003, pp. 109-122. J. Gwo�zdziewicz and A. P loski, On the Merle formula for polar invariants, Bull. Soc. Sci. Lett. L�od�z 41 (1991), no. 1-10, 61-67. H. Hironaka, Introduction to the theory of in�nitely near singular points, Consejo Superior de Investigaciones Cient���cas, Madrid, 1974, Memorias de Matematica del Instituto "Jorge Juan", No. 28. I. Luengo, A new proof of the Jung-Abhyankar theorem, J. Algebra 85 (1983), 399-409. A.N. Var�cenko, Zeta-function of monodromy and Newton's diagram, Invent. Math. 37 (1976), no. 3, 253-262.978-0-8218-4890-6https://hdl.handle.net/20.500.14352/45438Papers from the Conference on Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held in Jaca, June 22–26, 2009The concept of ν-quasi-ordinary power series, which is a generalization of quasi-ordinary power series, was first introduced by H. Hironaka. In the paper under review, the authors study ν-quasi-ordinary power series and give a factorization theorem for ν-quasi-ordinary power series in the first part. The proof of the theorem uses Newton maps. In the second part of the paper, using the factorization theorem, they introduce the Newton tree to encode the Newton process for any hypersurface singularity defined by a power series germ as in Notation 1.1. Finally, the authors describe a condition for two ν-quasi-ordinary power series to have an "intersection multiplicity " by using Newton trees and they can also compute this generalized intersection multiplicity, resultants and discriminant.engbook parthttp://www.ams.org/bookstore?fn=20&arg1=conmseries&ikey=CONM-538http://www.ams.org/home/pagerestricted access512.76/.77Quasi-ordinary power seriesresultantfactorisationGeometria algebraica1201.01 Geometría Algebraica