Eigenfunctions of the Fourier transform with specified zeros
Eigenfunctions of the Fourier transform with specified zeros
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具有指定零点的傅里叶变换的特征函数
DOI：
10.1017/s0305004120000249
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发表时间：
2019
影响因子：
0.8
通讯作者：
D. Hardin
中科院分区：
文献类型：
--
作者：
A. Feigenbaum;P. Grabner;D. Hardin
本征函数的傅里叶变换与规定的零发挥了重要作用，证明了E8和水蛭晶格给予最好的球包装在各自的尺寸8和24科恩，库马尔，米勒，拉琴科和维亚佐夫斯卡。用于线性规划参数的函数被构造为某些模和拟模形式的拉普拉斯变换。科恩和贡萨尔维斯使用类似的构造来寻找满足12维最优不确定性原理的函数。本文给出了一个统一的看法，这些建设和发展的机器，以找到潜在的形式在所有的尺寸可除4。此外，在这种情况下发生的准模形式的傅立叶系数的积极性进行了讨论。
Eigenfunctions of the Fourier transform with prescribed zeros played a major role in the proof that the E8 and the Leech lattice give the best sphere packings in respective dimensions 8 and 24 by Cohn, Kumar, Miller, Radchenko and Viazovska. The functions used for a linear programming argument were constructed as Laplace transforms of certain modular and quasimodular forms. Similar constructions were used by Cohn and Gonçalves to find a function satisfying an optimal uncertainty principle in dimension 12. This paper gives a unified view on these constructions and develops the machinery to find the underlying forms in all dimensions divisible by 4. Furthermore, the positivity of the Fourier coefficients of the quasimodular forms occurring in this context is discussed.