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arXiv · 2604.10605

Singularities of diagonals of Laurent series for rational functions

Dmitriy Pochekutov
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Abstract

We study the complete diagonal of the Laurent series expansion of a rational function in $n$-complex variables. For a denominator that is nondegenerate for its Newton polyhedron, we prove that the complete diagonal, initially defined in a logarithmically convex domain, can be analytically continued along any path in the $r$-dimensional complex torus that avoids an explicitly defined complex analytic set $L$ called the Landau variety. This variety is constructed as the union of discriminants associated with specific truncations of the denominator to the faces of its Newton polyhedron.

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Dmitriy Pochekutov. 2026-04-12. Singularities of diagonals of Laurent series for rational functions. https://arxiv.org/abs/2604.10605

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