Banerjee, Pradipto
(2014)
On Galois groups of generalized Laguerre polynomials whose discriminants are squares.
Journal of Number Theory, 141.
pp. 3658.
ISSN 0022314X
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Abstract
In this paper, we compute Galois groups over the rationals associated with generalized Laguerre polynomials Ln(∝)(x) whose discriminants are rational squares, where n and α are integers. An explicit description of the integer pairs ((n,∝)for which the discriminant of Ln(∝)(x) is a rational square was recently obtained by the author in a joint work with Filaseta, Finch and Leidy. Among these pairs ((n,∝), we show that for 2≤n≤5, the associated Galois group of Ln(∝)(x) is always.
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