Geodesic
Optimal asymptotic bounds for spherical designs
Andriy Bondarenko1 ; Danylo Radchenko2 ; Maryna Viazovska3
1 Centre de Recerca Matemàtica, Bellaterra (Barcelona), Spain, National Taras Shevchenko University, Kyiv, Ukraine, and Norwegian University of Science and Technology, Trondheim, Norway
2 Max Planck Institute for Mathematics, Bonn, Germany and National Taras Shevchenko, University, Kyiv, Ukraine
3 University of Cologne, Cologne, Germany and Max Planck Institute for Mathematics, Bonn, Germany
Annals of mathematics, Tome 178 (2013) no. 2, pp. 443-452

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 $d$.

DOI : 10.4007/annals.2013.178.2.2

Andriy Bondarenko 1 ; Danylo Radchenko 2 ; Maryna Viazovska 3

1 Centre de Recerca Matemàtica, Bellaterra (Barcelona), Spain, National Taras Shevchenko University, Kyiv, Ukraine, and Norwegian University of Science and Technology, Trondheim, Norway
2 Max Planck Institute for Mathematics, Bonn, Germany and National Taras Shevchenko, University, Kyiv, Ukraine
3 University of Cologne, Cologne, Germany and Max Planck Institute for Mathematics, Bonn, Germany 
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Andriy Bondarenko; Danylo Radchenko; Maryna Viazovska. Optimal asymptotic bounds for spherical designs. Annals of mathematics, Tome 178 (2013) no. 2, pp. 443-452. doi: 10.4007/annals.2013.178.2.2

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