Mahler Measure and Numerical Semigroups

In this talk, we first review some classical results in the theory of the Mahler measure. Using classical results and assuming Lehmer’s conjecture, we then provide a proof of a conjecture due to P. Moree and A. Herrera-Poyatos.

We conclude by presenting some open questions concerning potential connections between Lehmer’s problem and the Mahler measure of polynomials arising from numerical semigroups.