Margulis's bounded-degree Mahler measure conjecture

Let $p(x)\in\mathbb Z[x]$ be a monic non-cyclotomic polynomial, define its exponential Mahler measure by

$$m(p)=\prod_{|\alpha_i|>1}|\alpha_i|,$$

and let $d(p)$ be the number of roots of $p$ whose absolute value is greater than $1$:

$$d(p)=\#\{\alpha_i:|\alpha_i|>1\}.$$

Margulis's conjecture. There is a function $\ell:\mathbb N\to\mathbb R^{>0}$ such that $m(p)\geq1+\ell\bigl(d(p)\bigr)$ for every non-cyclotomic monic polynomial $p(x)\in\mathbb Z[x]$. This is presented as weaker than Lehmer's conjecture and is used to obtain a uniform lower bound on short closed geodesics in arithmetic locally symmetric manifolds; it remains open in the source.