A set of points on the sphere with small Riesz energy

Stefan Steinerberger

We construct a set of points $\left\{x_1,\dots ,x_n\right\}\subset {\mathbb{S}}^2$ such that $$ \sum_{i \neq j} \frac{1}{\|x_i - x_j\|^2} \leq \frac{n^2 \log{n}}{4} + cn^2 + O(n^{1…