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

2024/02/07 by Jenvrin, Jonathan
#11G50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.04908

Abstract

Amoroso and Masser proved that for every real ε> 0, there exists a constant c(ε)>0, such that for every algebraic number α with ℚ(α)/ℚ being 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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