Lehmer's problem for polynomials with odd coefficients
by
Michael Mossinghoff
Davidson College
Coauthors: Peter Borwein, Edward Dobrowolski, and Artūras Dubickas

Lehmer asked if there exist polynomials with integer coefficients having Mahler's measure approaching 1, but not equal to 1. We resolve this problem for the special case of polynomials with no cyclotomic factors whose coefficients are all congruent to 1 modulo a fixed integer m >= 2. We use similar methods to determine a lower bound in the problem of Schinzel and Zassenhaus on the largest root of such a polynomial, and to improve a lower bound on the height of an algebraic unit whose minimal polynomial splits completely over a p-adic field.

Date received: April 20, 2004