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arXiv · 1203.4976

A note on generators of number fields

Jeffrey D. Vaaler·Martin Widmer
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Abstract

We establish upper bounds for the smallest height of a generator of a number field $k$ over the rational field $\Q$. Our first bound applies to all number fields $k$ having at least one real embedding. We also give a second conditional result for all number fields $k$ such that the Dedekind zeta-function associated to the Galois closure of $k/\Q$ satisfies GRH. This provides a partial answer to a question of W. Ruppert.

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Jeffrey D. Vaaler, Martin Widmer. 2012-03-22. A note on generators of number fields. https://arxiv.org/abs/1203.4976

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