A Lehmer-type gap conjecture for bounded-coefficient polynomial sequences

Let $N\geq 1$ be a natural number. Let $P_{2n+2l}$ be any sequence of integer polynomials defined in the paper's equation (SeqPoly), with every coefficient having modulus at most $N$, and let its limit ratio be the ratio between the number of nonunimodular roots and the degree in the relevant limiting process.

Bounded-coefficient limit-ratio conjecture. If the limit ratio of such a sequence is strictly below some constant $c(N)>0$, then its limit ratio is equal to $0$.

This is presented as an analogue of Lehmer's conjecture. The paper notes that arbitrary closeness to zero is possible with unbounded coefficients, while its calculations and an earlier theorem motivate a positive gap for bounded coefficients; the assertion is not established in the supplied text.