On a certain family of generalized Laguerre polynomials

DOI10.1016/j.jnt.2004.03.004zbMath1053.11083OpenAlexW1970787745MaRDI QIDQ1876229

Elizabeth A. Sell

Publication date: 16 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2004.03.004

zbMATH Keywords

Newton polygonsGeneralized Laguerre polynomials

Mathematics Subject Classification ID

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 (20)

On the Galois group of generalized Laguerre polynomials ⋮ On a conjecture of Wilf ⋮ Classifying families of orthogonal polynomials having Galois group the alternating group ⋮ Harmonic divisors and rationality of zeros of Jacobi polynomials ⋮ Specializations of one-parameter families of polynomials ⋮ Irreducibility and Galois groups of generalized Laguerre polynomials \(L_n^{(- 1 - n - r)}(x)\) ⋮ Extension of Laguerre polynomials with negative arguments ⋮ 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 the Jacobians of Curves Defined by the Generalized Laguerre Polynomials ⋮ On the ranks of the Jacobians of curves defined by Jacobi polynomials ⋮ On Galois groups of a one-parameter orthogonal family of polynomials ⋮ Divisibility properties of generalized Laguerre polynomials ⋮ Laguerre polynomials with Galois group \(A_m\) for each \(m\) ⋮ Algebraic properties of a family of Jacobi polynomials ⋮ Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers ⋮ IRREDUCIBILITY CRITERIA FOR SUMS OF TWO RELATIVELY PRIME POLYNOMIALS

Cites Work

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• Some generalized Laguerre polynomials whose Galois groups are the alternating groups
• The Witt invariant of the form \(\text{Tr}(x^ 2)\)
• On blocks of twisted group algebras
• \(\tilde A_5\) and \(\tilde A_7\) are Galois groups over number fields
• On the Galois groups of the exponential Taylor polynomials
• Some \(\widetilde A_ n\)-extensions obtained from generalized Laguerre polynomials
• On a theorem by Serre
• On the irreducibility of the generalized Laguerre polynomials

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