2017/05/10 by Ignacio García-Marco, García-Marco, Ignacio, Pascal Koiran +3
Mathematics · #12D99 #26A75 #30A06 #Advanced Differential Equations and Dynamical Systems #Commutative Algebra (math.AC) #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1705.03842
openalex publication_date 2017/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We call shifted power a polynomial of the form (x-a)e. The main goal of this paper is to obtain broadly applicable criteria ensuring that the elements of a finite family F of shifted powers are linearly independent or, failing that, to give a lower bound on the dimension of the space of polynomials spanned by F. In particular, we give simple criteria ensuring that the dimension of the span of F is at least c.|F| for some absolute constant c<1. We also propose conjectures implying the linear independence of the elements of F. These conjectures are known to be true for the field of real numbers, but not for the field of complex numbers.