Algebraic properties of a family of Generalized Laguerre Polynomials
| dc.creator | Hajir, Farshid | |
| dc.date | 2004-06-15 | |
| dc.date.accessioned | 2026-07-07T05:09:16Z | |
| dc.date.available | 2026-07-07T05:09:16Z | |
| dc.description | We study the algebraic properties of Generalized Laguerre Polynomials for negative integral values of the parameter. For integers $r,n\geq 0$, we conjecture that $L_n^{(-1-n-r)}(x) = \sum_{j=0}^n \binom{n-j+r}{n-j}x^j/j!$ is a $\Q$-irreducible polynomial whose Galois group contains the alternating group on $n$ letters. That this is so for $r=n$ was conjectured in the 50's by Grosswald and proven recently by Filaseta and Trifonov. It follows from recent work of Hajir and Wong that the conjecture is true when $r$ is large with respect to $n\geq 5$. Here we verify it in three situations: i) when $n$ is large with respect to $r$, ii) when $r \leq 8$, and iii) when $n\leq 4$. The main tool is the theory of $p$-adic Newton Polygons. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406307 | |
| dc.identifier | http://arxiv.org/abs/math/0406307 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71568 | |
| dc.subject | Number Theory | |
| dc.subject | 11R09; 11R32 | |
| dc.title | Algebraic properties of a family of Generalized Laguerre Polynomials | |
| dc.type | text |