Extensions of Schur's irreducibility results

Laishrama, Shanta ; Shorey, T. N. (2011) Extensions of Schur's irreducibility results Indagationes Mathematicae, 21 (1-2). pp. 87-105. ISSN 0019-3577

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.indag.2011.03.002


We prove that the generalized Laguerre polynomials Ln(α)(x) with 0≤α≤50 are irreducible except for finitely many pairs (n,α) and that these exceptions are necessary. In fact, we consider a more general polynomials fa(x) of degree n. Except for explicitly given Initely many pairs (n; a), we show that fa(x) with 0 ≤ a ≤ 40 are either irreducible or linear polynomial times an irreducible polynomial of degree n −1. This is derived from a more general result proved in the paper.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Laguerre Polynomials; Irreducibility; Primes
ID Code:67771
Deposited On:31 Oct 2011 13:30
Last Modified:31 Oct 2011 13:30

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