Melle Hernández, AlejandroGusein-Zade, Sabir MedgidovichLuengo Velasco, Ignacio2023-06-202023-06-201998-040016-266310.1007/BF02482595https://hdl.handle.net/20.500.14352/57082Let f be a meromorphic function germ on (Cn+1, 0); that is, f = P/Q, where P,Q: (Cn+1, 0)! (C, 0) are holomorphic germs. The authors introduce a notion of Milnor fibers and monodromy operators of the germ f around zero and infinity. Based on their previous work [Comment. Math. Helv. 72 (1997), no. 2, 244–256; MR1470090 (98j:32043)] they write down formulas for the zetafunctions of the monodromy operators in terms of partial resolutions of a singularity. In the case where P and Q are non-degenerate relative to their Newton’s diagrams an analog of the formula from [A. N. Varchenko, Invent. Math. 37 (1976), no. 3, 253–262; MR0424806 (54 #12764)] for zeta functions of monodromy operators is obtained. In conclusion, two interesting examples with f = (x3 −xy)/y and f = (xyz +xp +yq +zr)/(xd +yd +zd) are discussed in detail.engjournal articlehttp://www.springerlink.com/content/0016-2663/open access512.7MonodromyGerm of meromorphic functionResolution of germMilnor fiberResolution of singularitiesMonodromy transformationZeta function of monodromyA'Campo formulapartial resolutionNewton diagramsGeometria algebraica1201.01 Geometría Algebraica