Gusein-Zade, Sabir MedgidovichLuengo Velasco, IgnacioMelle Hernández, Alejandro2023-06-202023-06-201999N. A’Campo, La fonction zˆeta d’une monodromie, Comment. Math. Helv. 50 (1975), 233–248. V.I. Arnold, S.M. Gusein-Zade, A.N. Varchenko, Singularities of Differentiable Maps, vol. II, Birkhäuser, Boston–Basel–Berlin, 1988. E. Artal-Bartolo, I. Luengo, A. Melle-Hernández, Milnor number at infinity, topology and Newton boundary of a polynomial function, Preprint (1997). S.M. Gusein-Zade, I. Luengo, A. Melle-Hernández, Partial resolutions and the zeta-function of a singularity, Comment. Math. Helv. 72 (1997), 244–256. S.M. Gusein-Zade, I. Luengo, A. Melle-Hernández, Zeta-functions for germs of meromorphic functions and Newton diagrams, Preprint of the Fields Institute for Research in Mathematical Sciences FI–ST 1997–005, to appear in Funct. Anal. and its Appl., 1998. S.M. Gusein-Zade, I. Luengo, A. Melle-Hernandez, On zeta-function of a polynomial at infinity, Preprint, XXX Mathematics Archives, math.AG/9801093. F. Pham, Vanishing homologies and the n variable saddlepoint method, Singularities, Proceedings of Symposia in Pure Mathematics, vol. 40, Part 2, A.M.S., Providence, RI, 1983, pp. 319–335. O.Y. Viro, Some integral calculus based on Euler characteristic, Topology and Geometry — Rohlin seminar. Lecture Notes in Math., vol. 1346, Springer, Berlin–Heidelberg–New York, 1988, pp. 127–138.1531-8605https://hdl.handle.net/20.500.14352/58416A meromorphic function on a compact complex analytic manifold defines a C∞ locally trivial bundle over the complement to a finite subset of the projective line CP1, the bifurcation set. The monodromy transformations of this bundle correspond to loops around the points of the bifurcation set. In this paper we show that the zeta functions of these monodromy transformations {reviewer's remark: the inverse of the one defined by A'Campo} can be expressed in local terms, namely as integrals of the zeta functions of meromorphic germs with respect to the Euler characteristic. A special case of a meromorphic function on the projective space CPn is a function defined by a polynomial in n variables. We describe some applications of our technique to polynomial functions.engjournal articlehttp://link.springer.com/journal/11501http://link.springer.com/restricted access514.76compact manifoldsmeromorphic functionscritical valuesMilnor fibrationmonodromyzeta-functionsbifurcationsEuler characteristicGrupos (Matemáticas)