HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

On the Galois groups of generalized Laguerre Polynomials

Abstract : For a positive integer n and a real number α, the generalized Laguerre polynomials are defined by L (α) n (x) = n j=0 (n + α)(n − 1 + α) · · · (j + 1 + α)(−x) j j!(n − j)!. These orthogonal polynomials are solutions to Laguerre's Differential Equation which arises in the treatment of the harmonic oscillator in quantum mechanics. Schur studied these Laguerre polynomials for their interesting algebraic properties. In this short article, it is shown that the Galois groups of Laguerre polynomials L(α)(x) is Sn with α ∈ {±1,±1,±2,±1,±3} except when (α,n) ∈ {(1,2),(−2,11),(2,7)}. The proof is based on ideas of p−adic Newton polygons.
Document type :
Journal articles
Complete list of metadata

Cited literature [5 references]  Display  Hide  Download

Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Tuesday, October 27, 2015 - 10:38:53 AM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Friday, April 28, 2017 - 5:55:40 AM


Explicit agreement for this submission




Shanta Laishram. On the Galois groups of generalized Laguerre Polynomials. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2014, Volume 37 - 2014, pp.8-12. ⟨10.46298/hrj.2014.1317⟩. ⟨hal-01220303⟩



Record views


Files downloads