Monodromies of singularities of the Hadamard and eñe product

Ricardo Pérez-Marco (1, 2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 CNRS - Centre National de la Recherche Scientifique

We prove that singularities with monodromies are preserved by Hadamard product, and we find an explicit formula for the monodromy of the singularities of the Hadamard product. We find similar formulas for the eñe product whose monodromy is better behaved. With these formulas we give new direct proofs of classical results and prove the invariance of interesting rings of functions by Hadamard multiplication and eñe product.

Mots clés: eñe product; Hadamard product; singularities with monodromy; transalgebraic class

Domaines: Variables complexes [math.CV]; Théorie des nombres [math.NT]

Ricardo Pérez-Marco. Monodromies of singularities of the Hadamard and eñe product. 2020. ⟨hal-02953330⟩