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Preprints, Working Papers, ... Year : 2024

Explicit lower bounds for the height in Galois extensions of number fields

Jonathan Jenvrin

Abstract

Amoroso and Masser proved that for every real ϵ > 0, there is a constant c(ϵ) > 0, with the property that, for every algebraic number α such that Q(α)/Q is a Galois extension, the height of α is either 0 or at least c(ϵ)[Q(α) : Q]-ϵ. In this article, we establish an explicit version of this theorem.
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Dates and versions

hal-04475302 , version 1 (23-02-2024)

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Public Domain

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Jonathan Jenvrin. Explicit lower bounds for the height in Galois extensions of number fields. 2024. ⟨hal-04475302⟩

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