English

The finiteness of computing the ultrametric Mahler measure

Number Theory 2025-04-02 v1

Abstract

Recent work of Fili and the author examines an ultrametric version of the Mahler measure, denoted M(α)M_\infty(\alpha) for an algebraic number α\alpha. We show that the computation of M(α)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(α)M_\infty(\alpha).

Keywords

Cite

@article{arxiv.1408.5043,
  title  = {The finiteness of computing the ultrametric Mahler measure},
  author = {Charles L. Samuels},
  journal= {arXiv preprint arXiv:1408.5043},
  year   = {2025}
}