4 problems

Schinzel–Zassenhaus–Boyd conjecture. There is a constant $T>1$ such that if $\alpha$ is not a root of unity, then

Composite-degree extremal reciprocal polynomial conjecture. If $R_{2p_i}(x)$ is the minimal polynomial of the extremal reciprocal algebraic integer of degree $2p_i$, then

Let $d\geq 17$ be prime with $d\equiv 5\pmod 6$. Define … Let an algebraic integer of degree $d$ that is not a root of unity be extremal if it has the minimum possible house among…

Let $\mathrm{mr}(d)$ be the minimum of the houses of reciprocal algebraic integers of degree $d$ that are not roots of unity. An algebraic integer attaining $\mathrm{mr}(d)$ is cal…