Geodesic
Mellin transforms for rational functions with quasi-elliptic denominators
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 6, pp. 738-750

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The paper deals with residue representations of $n$–dimensional Mellin transforms for rational functions with quasi-elliptic denominators. These representations are given by integrals over $(n-1)$-dimensional relative cycles. The amount of representations (or cycles) equals to the number of facets of the Newton polytope for the denominator of the rational function.
Keywords: multidimensional Mellin transform, amoeba.
Mots-clés : quasi-elliptic polynomial, Leray residue form 
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     title = {Mellin transforms for rational functions with quasi-elliptic denominators},
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Irina A. Antipova; Timofey A. Efimov; Avgust K. Tsikh. Mellin transforms for rational functions with quasi-elliptic denominators. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 6, pp. 738-750. http://geodesic.mathdoc.fr/item/JSFU_2023_16_6_a3/