On Lisbon integrals

Daniel Barlet (1, 2) , Teresa Monteiro Fernandes (3)

1 IUF - Institut universitaire de France
2 IECL - Institut Élie Cartan de Lorraine
3 ULISBOA - Universidade de Lisboa = University of Lisbon

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 ∈ C k and z ∈ 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.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Daniel Barlet, Teresa Monteiro Fernandes. On Lisbon integrals. Mathematische Zeitschrift, 2020, ⟨10.1007/s00209-020-02540-6⟩. ⟨hal-02161740⟩