The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere

Abstract

We survey known results and present estimates and conjectures for the next-order term in the asymptotics of the optimal logarithmic energy and Riesz $s$-energy of $N$ points on the unit sphere in ${\mathbb{R}}^{d+1}$, $d\ge 1$. The conjectures are based on analytic continuation assumptions (with respect to $s$) for the coefficients in the asymptotic expansion (as $N\to \infty$) of the optimal $s$-energy.

References in corpus (2)

• Ground states and formal duality relations in the Gaussian core model
• Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds

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