Note on Lisbon integrals and their associated D--modules

TL;DR

This paper explores the relationships between Lisbon integrals, trace functions, and trace forms, and their connections to D-modules, clarifying the mathematical structures linking these concepts.

Contribution

It explicitly details the links between three types of Lisbon integrals, trace functions, trace forms, and their associated D-modules, providing a clearer understanding of their interrelations.

Findings

Established the correspondence between Lisbon integrals and D-modules.

Clarified the role of trace functions and forms in this context.

Provided a unified framework for understanding these mathematical objects.

Abstract

The aim of this Note is to specify the links between the three kinds of Lisbon integrals, trace functions and trace forms with the corresponding D--modules.