  We give a Schinzel-Zassenhaus-type lower bound for the maximum modulus of
roots of a monic integer polynomial with all roots symmetric with respect to
the unit circle. Our results extend a recent work of Dimitrov, who proved the
general Schinzel-Zassenhaus conjecture by using the P\'olya rationality theorem
for a power series with integer coefficients, and some estimates for
logarithmic capacity (transfinite diameter) of sets. We use an enhancement of
P\'olya's result obtained by Robinson, which involves Laurent-type rational
functions with small supremum norms, thereby replacing the logarithmic capacity
with a smaller quantity. This smaller quantity is expressed via a weighted
Chebyshev constant for the set associated with Dimitrov's function used in
Robinson's rationality theorem. Our lower bound for the house confirms a
conjecture of Boyd.

Number Theory;Complex Variables