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Hyperuniform point sets on the sphere: probabilistic aspects
Monatshefte für Mathematik ( IF 0.8 ) Pub Date : 2020-06-24 , DOI: 10.1007/s00605-020-01439-y
Johann S. Brauchart , Peter J. Grabner , Wöden Kusner , Jonas Ziefle

We give a unified description of the modular and quasi-modular functions used in Viazovska's proof of the best packing bounds in dimension 8 and the proof by Cohn, Kumar, Miller, Radchenko, and Viazovska of the best packing bound in dimension 24. We show that necessarily modular forms have to be used to obtain these results. We extend these constructions to arbitrary dimensions divisible by 4.

中文翻译:

球体上的超均匀点集:概率方面

我们统一描述了 Viazovska 的第 8 维最佳包装界的证明以及 Cohn、Kumar、Miller、Radchenko 和 Viazovska 的第 24 维最佳包装界的证明中使用的模和准模函数。我们展示了必须使用模块化形式才能获得这些结果。我们将这些结构扩展到可被 4 整除的任意维度。
更新日期:2020-06-24
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