Formulating a conjecture for C_{s,d} in other dimensions

Identify a plausible conjectural form for the constant C_{s,d} governing the second term (or leading term for s>d) in the large-N asymptotic expansion of minimal Riesz s-energy for dimensions d beyond those with established or proposed lattice formulas (i.e., dimensions other than 1, 2, 4, 8, and 24).

Background

For d=1, 8, and 24, universal optimality results yield explicit lattice-based formulas for C_{s,d}; for d=2 and d=4, analogous lattice-based formulas are conjectured. Beyond these dimensions, no canonical conjectural structure is currently agreed upon.

The authors explicitly note that even the form of a conjecture for C_{s,d} is unknown in other dimensions, underscoring a gap in understanding the geometric or analytic objects controlling energy asymptotics.