On the irreducibility of a certain class of Laguerre polynomials (Q1394921)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the irreducibility of a certain class of Laguerre polynomials |
scientific article; zbMATH DE number 1934766
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the irreducibility of a certain class of Laguerre polynomials |
scientific article; zbMATH DE number 1934766 |
Statements
On the irreducibility of a certain class of Laguerre polynomials (English)
0 references
25 June 2003
0 references
It is shown that almost all generalized Laguerre polynomials \(L_m^{(m)}\) are irreducible over the rationals. This implies, due to a result of \textit{R. Gow} [J. Number Theory 31, 201-207 (1989; Zbl 0693.12009)], that for almost all even \(m\) the Galois group of these polynomials is the alternating group \(A_m\).
0 references
irreducibility
0 references
Laguerre polynomials
0 references
alternating group
0 references
Galois group
0 references
0.9724704
0 references
0.96184075
0 references
0.93237525
0 references
0.9322978
0 references
0.9297252
0 references
0.92610216
0 references
0.92487794
0 references
0 references
