Abstract
We study energy integrals and discrete energies on the sphere, in particular, analogues of the Riesz energy with the geodesic distance in place of the Euclidean, and we determine that the range of exponents for which uniform distribution optimizes such energies is different from the classical case. We also obtain a very general form of the Stolarsky principle, which relates discrete energies to certain L2 discrepancies, and prove optimal asymptotic estimates for both objects. This leads to sharp asymptotics of the difference between optimal discrete and continuous energies in the geodesic case, as well as new proofs of discrepancy estimates.
Original language | English (US) |
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Pages (from-to) | 3141-3166 |
Number of pages | 26 |
Journal | Transactions of the American Mathematical Society |
Volume | 372 |
Issue number | 5 |
DOIs | |
State | Published - Sep 1 2019 |
Bibliographical note
Publisher Copyright:© 2018 American Mathematical Society.