Linear stability of the elliptic relative equilibrium with (1 + n)-gon central configurations in planar n-body problem

We study the linear stability of [inline-formula]-gon elliptic relative equilibrium (ERE for short), that is the Kepler homographic solution with the [inline-formula]-gon central configurations. We show that for [inline-formula] and any eccentricity [inline-formula], the [inline-formula]-gon ERE is stable when the central mass m is large enough. Some linear instability results are given when m is small.