English

Distances between the conjugates of an algebraic number

Number Theory 2023-09-19 v1

Abstract

Given a fixed number field K, we give non-trivial lower bounds for the distance between the conjugates of any number a from K in terms of the Mahler measure M(a) of a. In the case that K is a cubic field, our bound is best possible in terms of M(a). Our proof is based on Roth's theorem.

Keywords

Cite

@article{arxiv.math/0408304,
  title  = {Distances between the conjugates of an algebraic number},
  author = {Jan-Hendrik Evertse},
  journal= {arXiv preprint arXiv:math/0408304},
  year   = {2023}
}

Comments

Latex file; 18 pages

R2 v1 2026-07-22T17:08:58.555Z