Optimal asymptotic bounds for spherical designs

Andriy Bondarenko; Danylo Radchenko; Maryna Viazovska

doi:https://doi.org/10.4007/annals.2013.178.2.2

Pages 443-452 from Volume 178 (2013), Issue 2 by Andriy Bondarenko, Danylo Radchenko, Maryna Viazovska

Abstract

In this paper we prove the conjecture of Korevaar and Meyers: for each $N\ge c_dt^d$, there exists a spherical $t$-design in the sphere $S^d$ consisting of $N$ points, where $c_d$ is a constant depending only on $d$.

Milestones

Received: 10 March 2011
Accepted: 11 March 2013
Published online: 7 September 2013

Authors

Andriy Bondarenko

Centre de Recerca Matemàtica, Bellaterra (Barcelona), Spain, National Taras Shevchenko University, Kyiv, Ukraine, and Norwegian University of Science and Technology, Trondheim, Norway

Danylo Radchenko

Max Planck Institute for Mathematics, Bonn, Germany and National Taras Shevchenko, University, Kyiv, Ukraine

Maryna Viazovska

University of Cologne, Cologne, Germany and Max Planck Institute for Mathematics, Bonn, Germany