On Galois groups of a one-parameter orthogonal family of polynomials
Pradipto Banerjee · Acta Arithmetica · 2018
For a fixed integer $t \gt 1$, we show that if $t$ is not equal to $2$, a square $\ge 4$, or three times a square, then the discriminant of the generalized Laguerre polynomial $L_{n}^{(s/t)}(x)$ is a nonzero square for at most finitely many pairs $(n,s)$.