Explicit spherical designs

被引:0
作者
Xiang, Ziqing [1 ,2 ]
机构
[1] Univ Georgia, Dept Math, Athens, GA 30602 USA
[2] Acad Sinica, Inst Math, Taipei, Taiwan
来源
ALGEBRAIC COMBINATORICS | 2022年 / 5卷 / 02期
关键词
Explicit construction; rational points; spherical designs; BOUNDS;
D O I
10.5802/alco.213
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Since the introduction of the notion of spherical designs by Delsarte, Goethals, and Seidel in 1977, finding explicit constructions of spherical designs had been an open problem. Most existence proofs of spherical designs rely on the topology of the spheres, hence their constructive versions are only computable, but not explicit. That is to say that these constructions can only give algorithms that produce approximations of spherical designs up to arbitrary given precision, while they are not able to give any spherical designs explicitly. Inspired by recent work on rational designs, i.e. designs consisting of rational points, we generalize the known construction of spherical designs that uses interval designs with Gegenbauer weights, and give an explicit formula of spherical designs of arbitrary given strength on the real unit sphere of arbitrary given dimension.
引用
收藏
页码:347 / 369
页数:24
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