Name
Abstract | ||
|---|---|---|
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. |
Year | Venue | DocType |
|---|---|---|
2017 | CoRR | Journal |
Volume | Citations | PageRank |
abs/1705.03842 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ignacio García-Marco | 1 | 0 | 0.68 |
| Pascal Koiran | 2 | 919 | 113.85 |
| Timothée Pecatte | 3 | 0 | 0.34 |