Minimal Mahler Measures

Abstract

We determine the minimal Mahler measure of a primitive irreducible noncyclotomic polynomial with integer coefficients and fixed degree D, for each even degree D ≤ 54. We also compute all primitive irreducible noncyclotomic polynomials with measure less than 1.3 and degree at most 44.

Keywords:

• Primary 11Y40
• Secondary 11R09
• Mahler measure
• Lehmer's question
• Chebyshev polynomial
• auxiliary function