The irreducibility of almost all Bessel polynomials (Q1092207)

The author proves that almost all Bessel polynomials are irreducible. This considerably strengthens a result of Grosswald that a positive proportion of Bessel polynomials are irreducible. A typical result of the author's is that for given n, if the product of the odd primes dividing n-1, the primes larger than 3 dividing \(n+2\) and the squares of the primes dividing \(n(n+1)\) exceeds \(n^ 2(n+1)^ 2\), then the nth Bessel polynomial is irreducible.