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تسجيل مستخدم جديدThe next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere
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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 $mathbb{R}^{d+1}$, $dgeq 1$. The conjectures are based on analytic continuation assumptions (with respect to $s$) for the coefficients in the asymptotic expansion (as $Nto infty$) of the optimal $s$-energy.
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Let $Lambda$ be a lattice in ${bf R}^d$ with positive co-volume. Among $Lambda$-periodic $N$-point configurations, we consider the minimal renormalized Riesz $s$-energy $mathcal{E}_{s,Lambda}(N)$. While the dominant term in the asymptotic expansion o
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