On Galois groups of generalized Laguerre polynomials whose discriminants are squares

Banerjee, Pradipto (2014) On Galois groups of generalized Laguerre polynomials whose discriminants are squares. Journal of Number Theory, 141. pp. 36-58. 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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