naa a22 4500 51081042X CHVBK 20180411083440.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s12220-011-9235-7 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9235-7 Mellin Transforms of Multivariate Rational Functions [Elektronische Daten] [Lisa Nilsson, Mikael Passare] This paper deals with Mellin transforms of rational functions g/f in several variables. We prove that the polar set of such a Mellin transform consists of finitely many families of parallel hyperplanes, with all planes in each such family being integral translates of a specific facial hyperplane of the Newton polytope of the denominator f. The Mellin transform is naturally related to the so-called coamoeba $\mathcal{A}'_{f}:=\mathrm{Arg}(Z_{f})$ , where Z f is the zero locus of f and Arg denotes the mapping that takes each coordinate to its argument. In fact, each connected component of the complement of the coamoeba $\mathcal{A}'_{f}$ gives rise to a different Mellin transform. The dependence of the Mellin transform on the coefficients of f, and the relation to the theory of A-hypergeometric functions is also discussed in the paper. Mathematica Josephina, Inc., 2011 Mellin transform nationallicence Coamoeba nationallicence Hypergeometric function nationallicence Nilsson Lisa Mathematical Sciences, Chalmers University of Technology and Gothenburg University, 412 96, Gothenburg, Sweden aut Passare Mikael Department of Mathematics, Stockholm University, 106 91, Stockholm, Sweden aut Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 24-46 1050-6926 23:1<24 2013 23 12220 https://doi.org/10.1007/s12220-011-9235-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9235-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nilsson Lisa Mathematical Sciences, Chalmers University of Technology and Gothenburg University, 412 96, Gothenburg, Sweden aut NATIONALLICENCE 700 1- Passare Mikael Department of Mathematics, Stockholm University, 106 91, Stockholm, Sweden aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 24-46 1050-6926 23:1<24 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer