The next-order term for optimal Riesz and logarithmic energy asymptotics   on the sphere
  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 $\mathbb{R}^{d+1}$, $d\geq 1$. 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. 
J. S. Brauchart, D. P. Hardin, and E. B. Saff
math-ph math.MP