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