THE NEXT-ORDER TERM FOR OPTIMAL RIESZ AND LOGARITHMIC ENERGY ASYMPTOTICS ON THE SPHERE

Dedicated to Paco Marcellán on the occasion of his 60-th birthday. Abstract. 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 Rd+1, d ≥ 1. The conjectures are based on analytic continu-ation assumptions (with respect to s) for the coefficients in the asymptotic expansion (as N →∞) of the optimal s-energy