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Communications in Number Theory and Physics
Volume 18 (2024)
Number 2
Vector spaces of generalized Euler integrals
Pages: 327 – 370
DOI: https://dx.doi.org/10.4310/CNTP.2024.v18.n2.a2
Authors
Abstract
We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman integrals from particle physics, this has been investigated using tools from homological algebra and the theory of $D$-modules. We present an overview and uncover new relations between these approaches. We also provide new algorithmic tools.
Keywords
generalized Euler integrals, twisted de Rham cohomology, Mellin transform, GKZ systems
2010 Mathematics Subject Classification
14-xx, 81-xx
With an appendix by Saiei-Jaeyeong Matsubara-Heo
Received 15 November 2022
Accepted 2 April 2024
Published 15 July 2024