Some \(\widetilde A_ n\)-extensions obtained from generalized Laguerre polynomials
type: Item
instance of: scholarly article
title: Some \(\widetilde A_ n\)-extensions obtained from generalized Laguerre polynomials
zbMATH Open document ID: 0829.12004
author: Farshid Hajir
published in: Journal of Number Theory
publication date: 1996-01-22T00:00:00Z
review text: Let \(L(x,\lambda)\) be the \(n\)-th degree generalized Laguerre polynomial. It is proved that for \(n\geq 14\) the Galois group of \(f(x)=L(x,-2-n)\) is \(A_n\) if \(n\equiv 1\pmod 4\), and \(S_n\) otherwise. Moreover it is proved that the splitting field of \(f(x)\) can be embedded in a field with absolute Galois group isomorphic to \(\widetilde A_n\), the double cover of \(A_n\), if and only if \(n\equiv 1\pmod 8\).
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 729072
zbMATH Keywords: embedding
zbMATH Keywords: inverse Galois theory
zbMATH Keywords: generalized Laguerre polynomial
zbMATH Keywords: Galois group
reviewed by: Nuria Vila
MaRDI profile type: Publication
full work available at URL: jnth.1995.1015
OpenAlex ID: W2084125712
DOI: 10.1006/JNTH.1995.1015
description: scientific article; zbMATH DE number 729072