Mellin transforms of multivariate rational functions
2013 (English)In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 23, no 1, 24-46 p.Article in journal (Refereed) Published
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 , 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 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.
Place, publisher, year, edition, pages
2013. Vol. 23, no 1, 24-46 p.
Mellin transform, Coamoeba, Hypergeometric function
IdentifiersURN: urn:nbn:se:su:diva-88300DOI: 10.1007/s12220-011-9235-7ISI: 000313444100002OAI: oai:DiVA.org:su-88300DiVA: diva2:612169