English

The infimum in the metric Mahler measure

Number Theory 2019-08-15 v1

Abstract

Dubickas and Smyth defined the metric Mahler measure on the multiplicative group of non-zero algebraic numbers. The definition involves taking an infimum over representations of an algebraic number α\alpha by other algebraic numbers. We verify their conjecture that the infimum in its definition is always achieved as well as establish its analog for the ultrametric Mahler measure.

Keywords

Cite

@article{arxiv.1408.4165,
  title  = {The infimum in the metric Mahler measure},
  author = {Charles L. Samuels},
  journal= {arXiv preprint arXiv:1408.4165},
  year   = {2019}
}