Number fields without small generators

DOI10.1017/S0305004115000298zbMath1371.11141arXiv1410.5258OpenAlexW3106365391MaRDI QIDQ5360345

Martin Widmer, Jeffrey D. Vaaler

Publication date: 28 September 2017

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.5258

Mathematics Subject Classification ID

Algebraic numbers; rings of algebraic integers (11R04) Other analytic theory (11R47)

Related Items (6)

Minimal Mahler measure in cubic number fields ⋮ Minimal Mahler measures for generators of some fields ⋮ Northcott numbers for the weighted Weil heights ⋮ Bounds for the ℓ-torsion in class groups ⋮ An effective Chebotarev density theorem for families of number fields, with an application to \(\ell \)-torsion in class groups ⋮ Average bounds for the \(\ell\)-torsion in class groups of cyclic extensions

Cites Work

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• The density of discriminants of quintic rings and fields
• Lower bounds for height functions
• Northcott's theorem on heights. I: A general estimate
• Small generators of number fields
• A note on Siegel's lemma over number fields
• The number of extensions of a number field with fixed degree and bounded discriminant
• Counting points of fixed degree and bounded height
• Density of discriminants of cubic extensions.
• A note on generators of number fields

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