Irreducibility of extensions of Laguerre Polynomials

2019/01/04 by Laishram, Shanta, Nair, Saranya G., Shorey, Tarlok Nath
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1901.01072

Abstract

For integers a₀,a₁,…,a_n with |a₀a_n|=1 and either α=u with 1≤ u ≤ 50 or α=u+ (1)/(2) with 1 ≤ u ≤ 45, we prove that ψ_n^(α)(x;a₀,a₁,⋯,a_n) is irreducible except for an explicit finite set of pairs (u,n). Furthermore all the exceptions other than n=2¹²,α=89/2 are necessary. The above result with 0≤α≤ 10 is due to Filaseta, Finch and Leidy and with α∈ \-1/2,1/2\ due to Schur.

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