Irreducibility of generalized Laguerre polynomials $L_n^{(1/2+u)}(x^2)$ with $-18 \leq u \leq -2$
Volume 184 / 2018
Acta Arithmetica 184 (2018), 363-383
MSC: Primary 11A41, 11B25, 11N05, 11N13, 11C08, 11Z05.
DOI: 10.4064/aa170726-7-8
Published online: 7 September 2018
Abstract
We consider the irreducibility of generalized Laguerre polynomials $ L_n^{(1/2+u)}(x^2)$ when $u$ is a negative integer. In 1926 Schur proved that these polynomials are irreducible when $u\in \{0,-1\}$. We study irreducibility of more general polynomials and as a consequence prove that $ L_n^{(1/2+u)}(x^2)$ are irreducible when $-18 \leq u \leq -2.$
