Stability of the regular n-gon rotating equilibria with logarithm interaction

We study the linear stability of regular n-gon rotating equilibria in the n-body problem with logarithm interaction. In the presence of a central mass M, linear stability is insured if M is bounded below and above by constants depending on the number and mass of the (equal) outer n bodies. Moreover, we provide explicit equations of these bounds. In the absence of a central mass we find that the regular n-gon is linearly stable for n =2,3,… 6 only.