Classifying families of orthogonal polynomials having Galois group the alternating group

DOI10.1016/j.jnt.2021.12.009OpenAlexW4207074554WikidataQ114156612 ScholiaQ114156612MaRDI QIDQ2161325

Pradipto Banerjee, Ranjan Bera

Publication date: 4 August 2022

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2021.12.009

zbMATH Keywords

Galois groupsirreducibilityalternating groupgeneralized Laguerre polynomials

Mathematics Subject Classification ID

Galois theory (11R32) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Polynomials in number theory (11C08)

Cites Work

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• On Galois groups of generalized Laguerre polynomials whose discriminants are squares
• Some generalized Laguerre polynomials whose Galois groups are the alternating groups
• Laguerre polynomials with Galois group \(A_m\) for each \(m\)
• On a generalization of a conjecture of Grosswald
• On the Galois group of generalized Laguerre polynomials
• Some \(\widetilde A_ n\)-extensions obtained from generalized Laguerre polynomials
• On a certain family of generalized Laguerre polynomials
• The irreducibility of all but finitely many Bessel polynomials
• On classifying Laguerre polynomials which have Galois group the alternating group
• Approximate formulas for some functions of prime numbers
• Algebraic Properties of a Family of Generalized Laguerre Polynomials
• The irreducibility of the Bessel polynomials
• Die Seltenheit der reduziblen Gleichungen und der Gleichungen mit Affekt
• Primes in short intervals

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