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In this article, we present the integral representations of the power seriesdiagonals. Such representations are obtained by lowering the integrationmultiplicity for the previously known integral representation. The procedure iscarried out within the framework of Leray's residue theory. The concept of theamoeba of the complex analytical hypersurface plays an essential role in theconstruction of new integral representations.

A List of Integral Representations for Diagonals of Power Series of Rational Functions