  We consider the roots of uniformly chosen complex and real reciprocal
polynomials of degree $N$ whose Mahler measure is bounded by a constant. After
a change of variables this reduces to a generalization of Ginibre's complex and
real ensembles of random matrices where the weight function (on the eigenvalues
of the matrices) is replaced by the exponentiated equilibrium potential of the
interval $[-2,2]$ on the real axis in the complex plane. In the complex (real)
case the random roots form a determinantal (Pfaffian) point process, and in
both cases the empirical measure on roots converges weakly to the arcsine
distribution supported on $[-2,2]$. Outside this region the kernels converge
without scaling, implying among other things that there is a positive expected
number of outliers away from $[-2,2]$. These kernels, as well as the scaling
limits for the kernels in the bulk $(-2,2)$ and at the endpoints $\{-2,2\}$ are
presented. These kernels appear to be new, and we compare their behavior with
related kernels which arise from the (non-reciprocal) Mahler measure ensemble
of random polynomials as well as the classical Sine and Bessel kernels.
