Laguerre polynomials with Galois group \(A_m\) for each \(m\)

DOI10.1016/j.jnt.2011.09.012zbMath1287.11123OpenAlexW2017507118MaRDI QIDQ765164

Travis Kidd, Ognian Trifonov, Michael Filaseta

Publication date: 19 March 2012

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2011.09.012

zbMATH Keywords

Galois groupNewton polygonLaguerre polynomialsirreducible polynomial

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)

Related Items (13)

Classifying families of orthogonal polynomials having Galois group the alternating group ⋮ Families of Laguerre polynomials with alternating group as Galois group ⋮ Irreducibility and Galois groups of generalized Laguerre polynomials \(L_n^{(- 1 - n - r)}(x)\) ⋮ On Galois groups of generalized Laguerre polynomials whose discriminants are squares ⋮ Irreducibility criteria for the sum of two relatively prime multivariate polynomials ⋮ On two conjectures of irreducible polynomials ⋮ Irreducibility of generalized Laguerre polynomials \(L_n^{(\frac{1}{2} + u)}(x)\) with integer \(u\) ⋮ On classifying Laguerre polynomials which have Galois group the alternating group ⋮ On Galois groups of a one-parameter orthogonal family of polynomials ⋮ Extensions of Schur's irreducibility results ⋮ Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers ⋮ IRREDUCIBILITY CRITERIA FOR SUMS OF TWO RELATIVELY PRIME POLYNOMIALS ⋮ On the Galois theory of generalized Laguerre polynomials and trimmed exponential

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