Estimates for logarithmic and Riesz energies for spherical $t$-designs

Abstract

In this paper we find asymptotic equalities for the discrete logarithmic energy of sequences of well separated spherical $t$-designs on the unit sphere ${\mathbb{S}}^d\subset {\mathbb{R}}^{d+1}$, $d\ge 2$. Also we establish exact order estimates for discrete Riesz $s$-energy, $s\ge d$, of sequences of well separated spherical $t$-designs.

16 pages