COUNTING INTEGER REDUCIBLE POLYNOMIALS WITH BOUNDED MEASURE

The purpose of this work is to give an asymptotic formula for the number of integer reducible polynomials with fixed degree d >= 2 and Mahler measure bounded above by T and also.for the number of such monic polynomials as T -> infinity.We also consider the case of monic polynomials which have all their roots in the disc vertical bar z vertical bar <= R and find asymptotics for the number of such reducible polynomials too as R -> infinity. In all cases the constants in the main terms are related to the constants of the corresponding counting formulas for the number of such irreducible polynomials due to CHERN and VAALER (in case of Mahler measure) and AKIYAMA and PETHO (in case of a disc).