  The Riesz $s$-energy of an $N$-point configuration in the Euclidean space
$\mathbb{R}^{p}$ is defined as the sum of reciprocal $s$-powers of all mutual
distances in this system. In the limit $s\to0$ the Riesz $s$-potential $1/r^s$
($r$ the Euclidean distance) governing the point interaction is replaced with
the logarithmic potential $\log(1/r)$. In particular, we present a conjecture
for the leading term of the asymptotic expansion of the optimal
$\IL_2$-discrepancy with respect to spherical caps on the unit sphere in
$\mathbb{R}^{d+1}$ which follows from Stolarsky's invariance principle [Proc.
Amer. Math. Soc. 41 (1973)] and the fundamental conjecture for the first two
terms of the asymptotic expansion of the optimal Riesz $s$-energy of $N$ points
as $N \to \infty$.
