Geodesic
A list of integral representations for diagonals of power series of rational functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 5, pp. 624-631

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In this paper we present integral representations for the diagonals of power series. Such representations are obtained by lowering the multiplicity of integration for the previously known integral representation. The procedure for reducing the order of integration is carried out in the framework of the Leray theory of multidimensional residues. The concept of the amoeba of a complex analytic hypersurface plays a special role in the construction of new integral representations.
Keywords: multidimensional power series, complex integral, integral representation, amoeba, Taylor series, diagonal of a power series. 
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     title = {A list of integral representations for diagonals of power series of rational functions},
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Artem V. Senashov. A list of integral representations for diagonals of power series of rational functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 5, pp. 624-631. http://geodesic.mathdoc.fr/item/JSFU_2021_14_5_a9/