Let $\alpha,\beta\in\overline{\mathbb Q}$. Denote by $h(\alpha)$ the house $\alpha$, that is the maximum of $|\sigma(\alpha)|$ when $\sigma$ describes $\mathrm{Gal}(\overline{\mathbb Q}/\mathbb Q)$. It is easy to prove that $$h(\alpha+\beta)\le h(\alpha)+h(\beta)\text{ and }h(\alpha\beta)\le h(\alpha)+h(\beta).$$ But I do not find an estimation of $h(\alpha/\beta)$. Does anyone know such a formula?
2026-03-25 22:03:49.1774476229
House of the inverse
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