A note on generators of number fields

2012/03/22 by Jeffrey D. Vaaler, Vaaler, Jeffrey D., Martin Widmer +1
Mathematics · Social Sciences · #11G50 #11R04 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.1203.4976

openalex publication_date 2012/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Small generators of number fields
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