On a certain family of generalized Laguerre polynomials |
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Authors: | Elizabeth A Sell |
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Affiliation: | University of North Carolina at Chapel Hill, CB #3250, Phillips Hall, Chapel Hill, NC 27599, USA |
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Abstract: | Following the work of Schur and Coleman, we prove the generalized Laguerre polynomial is irreducible over the rationals for all n?1 and has Galois group An if n+1 is an odd square, and Sn otherwise. We also show that for certain negative integer values of α and certain congruence classes of n modulo 8, the splitting field of Ln(α)(x) can be embedded in a double cover. |
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Keywords: | Generalized Laguerre polynomials Newton polygons |
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