The finiteness of computing the ultrametric Mahler measure
  Recent work of Fili and the author examines an ultrametric version of the Mahler measure, denoted $M_\infty(\alpha)$ for an algebraic number $\alpha$. We show that the computation of $M_\infty(\alpha)$ can be reduced to a certain search through a finite set. Although it is a open problem to record the points of this set in general, we provide some examples where it is reasonable to compute and our result can be used to determine $M_\infty(\alpha)$. 
Charles L. Samuels
math.NT