1. Monodromies of singularities of the Hadamard and eñe product
- Author
-
Pérez-Marco, Ricardo, Pérez-Marco, Ricardo, Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)
- Subjects
singularities with monodromy ,Hadamard product ,[MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV] ,eñe product ,[MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] ,transalgebraic class ,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] ,[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT] - Abstract
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.
- Published
- 2020