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

TL;DR

This paper introduces new integral representations for the diagonals of power series of rational functions, utilizing Leray's residue theory and the concept of amoebas to simplify existing methods.

Contribution

It provides a novel approach to derive integral representations with reduced integration complexity using advanced complex analysis techniques.

Findings

New integral representations for power series diagonals

Reduced integration multiplicity in the representations

Application of amoeba theory in complex analysis

Abstract

In this article, we present the integral representations of the power series diagonals. Such representations are obtained by lowering the integration multiplicity for the previously known integral representation. The procedure is carried out within the framework of Leray's residue theory. The concept of the amoeba of the complex analytical hypersurface plays an essential role in the construction of new integral representations.