8 problems

Smallest positive limit-point conjecture. If $P_{2n}$ is a sum of $2k+3$ monomials, with $a_0\ne 0$, then

Let an extremal reciprocal primitive be an extremal reciprocal algebraic integer that is primitive, and let an octanomial be a polynomial with eight nonzero monomials. Octanomial e…

Let $d$ be an even natural number, and let $P_d(x)$ be the minimal polynomial of an extremal reciprocal algebraic integer of degree $d$. A polynomial is primitive in the sense used…

Let $\alpha$ be a reciprocal algebraic integer that is not a root of unity, and let $d=\deg(\alpha)\geq 2$. Let $\mathrm{mr}^d(d)$ denote the relevant degree-$d$ extremal reciproca…

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 $\mathrm{mr}(d)$ 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…

Let $P$ be a reciprocal polynomial whose zero locus has genus $1$. The Mahler measure $m(P)$ is the quantity associated with $P$, and formulas analogous to the formulas referred to…

A Laurent polynomial is reciprocal when it is invariant under the relevant reciprocal involution, and a formula is of mixed type when the Mahler measure has the form … for a Dirich…