On some polynomials allegedly related to the abc conjecture, by Alexandr Borisov

This paper has appeared in Acta Arith. 84 (1998), no. 2, 109-128, and so the dvi version has been removed. In this paper we introduce some polynomials that are probably related to the Masser-Oesterle $abc$ conjecture as they appear when one tries to follow the easy proofs of the corresponding theorem for polynomials. We study the distribution of their roots in usual complex and p-adic complex numbers for primes dividing $abc$. Using this information we prove that almost all of these polynomials (in the sense of natural density) are irreducible.

Alexandr Borisov <borisov@math.uga.edu>