Divisibility properties of generalized Laguerre polynomials

In this paper we give effective upper bounds for the degree k of divisors (over ℚ) of generalized Laguerre polynomials Lαn(x), i.e. of for α = −tn − s − 1 and α = tn + s with t,s ∈ ℕ, t = O(log k), s = O(k log k) and k sufficiently large.