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arXiv · 2505.12458

Spectral Decomposition of Euler-Mellin Integrals

Martin Helmer·Felix Tellander
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Abstract

We consider the spectral decomposition of singularities of integrals and their integrands. Our results apply to any integral of Euler-Mellin type, and thus especially to every scalar Feynman integral. Specifically we provide for both the integrand and integral respectively; two explicit constructions of the characteristic variety and characteristic cycle of the constructible function and $D$-module they are associated with. From this we also obtain the singular locus or Landau singularities of the integral. En route we give a simple procedure to compute the local Euler obstruction function of a variety, and using this, to compute the Euler characteristic of the complex link of a Whitney stratum.

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Martin Helmer, Felix Tellander. 2025-05-18. Spectral Decomposition of Euler-Mellin Integrals. https://arxiv.org/abs/2505.12458

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