On Lisbon integrals

Abstract

We introduce a family of integral transforms, the Lisbon Integrals, which naturally arise in the study of the affine space of unitary polynomials P s (z) where s \(\in\) C k and z \(\in\) C, s i identified to the i-th symmetric function of the roots of P s (z). We completely determine the D-module (or system of partial differential equations) the Lisbon Integrals satisfy and prove that they are their unique global solutions of this D-module.