On Galois groups of generalized Laguerre polynomials whose discriminants are squares

DOI10.1016/j.jnt.2014.01.009zbMath1322.11116OpenAlexW2089560761MaRDI QIDQ402618

Pradipto Banerjee

Publication date: 28 August 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2014.01.009

zbMATH Keywords

Galois groupirreducibility of polynomialsgeneralized Laguerre polynomials

Mathematics Subject Classification ID

Galois theory (11R32) Polynomials (irreducibility, etc.) (11R09)

Related Items (3)

Classifying families of orthogonal polynomials having Galois group the alternating group ⋮ Families of Laguerre polynomials with alternating group as Galois group ⋮ On Galois groups of a one-parameter orthogonal family of polynomials

Uses Software

• SageMath

Cites Work

• Unnamed Item
• Some generalized Laguerre polynomials whose Galois groups are the alternating groups
• Laguerre polynomials with Galois group \(A_m\) for each \(m\)
• On the Galois group of generalized Laguerre polynomials
• Specializations of one-parameter families of polynomials
• Some \(\widetilde A_ n\)-extensions obtained from generalized Laguerre polynomials
• On a certain family of generalized Laguerre polynomials
• On classifying Laguerre polynomials which have Galois group the alternating group
• Approximate formulas for some functions of prime numbers
• An Elementary Test for the Galois Group of a Quartic Polynomial
• Algebraic Properties of a Family of Generalized Laguerre Polynomials
• Class numbers of imaginary quadratic fields
• On the irreducibility of the generalized Laguerre polynomials
• THE DIOPHANTINE EQUATIONS x³=Ny²±1

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