An unsolved question surrounding the generalized Laguerre polynomial \(L_n^{(n)}(x)\)

DOI10.1007/s11139-024-00932-4MaRDI QIDQ6631609

Pradipto Banerjee

Publication date: 1 November 2024

Published in: The Ramanujan Journal (Search for Journal in Brave)

zbMATH Keywords

Galois groupirreducibilityalternating 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) Polynomials (irreducibility, etc.) (11R09)

Cites Work

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• On Galois groups of generalized Laguerre polynomials whose discriminants are squares
• Affektlose Gleichungen in der Theorie der Laguerreschen und Hermiteschen Polynome.
• Some generalized Laguerre polynomials whose Galois groups are the alternating groups
• Laguerre polynomials with Galois group \(A_m\) for each \(m\)
• Sur quelques cas d'irréductibilité des polynomes à coefficients rationnels.
• Gleichungen ohne Affekt.
• Einige Sätze über Primzahlen mit Anwendungen auf Irreduzibilitätsfragen. I, II.
• 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
• Classifying families of orthogonal polynomials having Galois group the alternating group
• Die Seltenheit der reduziblen Gleichungen und der Gleichungen mit Affekt.
• On the factorization of consecutive integers
• Algebraic Properties of a Family of Generalized Laguerre Polynomials

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