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Irreducibility of generalized Laguerre polynomials $L_n^{(1/2+u)}(x^2)$ with $-18 \leq u \leq -2$

Volume 184 / 2018

Saranya G. Nair, T. N. Shorey 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 $-18 \leq u \leq -2.$

Authors

  • Saranya G. NairStat-Math Unit
    Indian Statistical Institute
    8th Mile Mysore Road
    Bangalore, 560059, India
    e-mail
  • T. N. ShoreyNational Institute of Advanced Studies
    IISc Campus
    Bangalore, 560012, India
    e-mail

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