The Riesz energy of the $N$-th roots of unity: an asymptotic expansion for large $N$

J. S. Brauchart, D. P. Hardin, E. B. Saff

We derive the complete asymptotic expansion in terms of powers of $N$ for the Riesz $s$-energy of $N$ equally spaced points on the unit circle as $N\to \infty$. For $s\ge -2$, such…