A note on generators of number fields
Number Theory
2012-03-23 v1
Abstract
We establish upper bounds for the smallest height of a generator of a number field over the rational field . Our first bound applies to all number fields having at least one real embedding. We also give a second conditional result for all number fields such that the Dedekind zeta-function associated to the Galois closure of satisfies GRH. This provides a partial answer to a question of W. Ruppert.
Cite
@article{arxiv.1203.4976,
title = {A note on generators of number fields},
author = {Jeffrey D. Vaaler and Martin Widmer},
journal= {arXiv preprint arXiv:1203.4976},
year = {2012}
}