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

Daniele Agostini (Universität Tübingen, Germany)

Claudia Fevola (MPI-MiS Leipzig and Université Paris-Saclay, Inria, Palaiseau, France)

Anna-Laura Sattelberger (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)

Simon Telen (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)

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

Full Text (PDF format)

With an appendix by Saiei-Jaeyeong Matsubara-Heo

Received 15 November 2022

Accepted 2 April 2024

Published 15 July 2024