Large integer polynomials in several variables.

For every sufficiently large positive integer D, we construct a family of irreducible integer polynomials of degree D in n variables whose Mahler measures are bounded by D and whose values at (1, ... , 1) are greater than exp {(1/9n) Dn/(n + 1)}. This shows that an upper bound for the height of integer irreducible polynomials in terms of their degree and Mahler measure obtained by Amoroso and Mignotte is sharp up to a logarithmic factor.