2023/11/22 by Daniel Barlet, Barlet, Daniel
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2311.13259
openalex publication_date 2023/11/22 · openalex created_date 2023/11/24 · openalex updated_date 2026/07/28
We give, using higher Bernstein polynomials defined in our paper [2], a stronger version of our previous result in [1] whose converse is proved in [2] and we give some complements to the results in [2] which help to compute these higher order Bernstein polynomials. Then we show some non trivial examples where we determine the root of the second Bernstein polynomial which is not a double root of the full Bernstein polynomial and where the main theorem of [2] applies and localizes where a double pole exists for the meromorphic extension of the (conjugate) analytic functional given by polar parts of ω ' → |f | 2λ f --h ρω ∧ ω' when h ∈ N is large enough.