Tuesday, February 21, 2012

1202.4037 (J. S. Brauchart et al.)

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

J. S. Brauchart, D. P. Hardin, E. B. Saff
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.
View original: http://arxiv.org/abs/1202.4037

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