On Cimmino Integrals as Residues of Zeta Functions

TL;DR

This paper links Cimmino integrals, used for solving linear systems, to residues of zeta-like functions, providing a novel theoretical perspective that could impact both analysis and computation.

Contribution

It establishes a new connection between Cimmino integrals and residues of zeta functions, enhancing understanding of integral representations in linear algebra.

Findings

Cimmino integrals are related to residues of zeta functions

Provides a new theoretical framework for linear system solutions

Potential implications for computational methods

Abstract

The following paper is a variation on a theme of Gianfranco Cimmino on some integral representation formulas for the solution of a linear equations system. Cimmino was probably motivated for giving a representation formula suitable not only for theoretical investigations but also for applied computation. In this paper we will prove that the Cimmino integrals are strictly related to the residues of some zeta-like functions associated to the linear system.