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Mellin Transforms of Multivariate Rational Functions by Nilsson, Lisa; Passare, Mikael is a scholarly article available to read on EtoBox.

What is Mellin Transforms of Multivariate Rational Functions about?

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 $\mathcal{A}'_f:=\text{Arg}\,(Z_f)$, where $Z_f$ is the zero locus of $f$ and $\text{Arg}$ 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.

Author

Nilsson, Lisa; Passare, Mikael

Published

2010

Language

EN