Northcott numbers for the house and the Weil height

Fabien Pazuki, Niclas Technau, Martin Widmer

For an algebraic number $\alpha$ and $\gamma \in \mathbb{R}$, $h(\alpha )$ be the (logarithmic) Weil height, and $h_{\gamma }(\alpha )=(\mathrm{deg}\alpha {)}^{\gamma }h(\alpha )$ be the $\gamma$-weighted (logarithmic) Weil height of $\alpha$.…