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

Jonathan Jenvrin
Feb 2024
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摘要原文
Amoroso and Masser proved that for every real $\epsilon > 0$, there exists a constant $c(\epsilon)>0$, such that for every algebraic number $\alpha$ with $\mathbb{Q}(\alpha)/\mathbb{Q}$ being a Galois extension, the height of $\alpha$ is either 0 or at least $c(\epsilon) [\mathbb{Q}(\alpha):\mathbb{Q}]^{-\epsilon}$. In this article we establish an explicit version of this theorem.
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