On the Galois group 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 | Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be ``large.'' For a fixed $α\in \Q - \Z_{<0}$, Filaseta and Lam have shown that the $n$th degree Generalized Laguerre Polynomial $L_n^{(α)}(x) = \sum_{j=0}^n \binom{n+α}{n-j}(-x)^j/j!$ is irreducible for all large enough $n$. We use our criterion to show that, under these conditions, the Galois group of $\La$ is either the alternating or symmetric group on $n$ letters, generalizing results of Schur for $α=0,1$. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406308 | |
| dc.identifier | http://arxiv.org/abs/math/0406308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71569 | |
| dc.subject | Number Theory | |
| dc.subject | 11R32; 11R09 | |
| dc.title | On the Galois group of Generalized Laguerre Polynomials | |
| dc.type | text |