Asymptotics of variance of the lattice point count

被引：0
|
作者：
Jiří Janáček
机构：
[1] Academy of Sciences of the Czech Republic,Institute of Physiology
来源：
Czechoslovak Mathematical Journal | 2008年 / 58卷
关键词：
point lattice; Fourier transform; volume; variance;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The variance of the number of lattice points inside the dilated bounded set rD with random position in ℝd has asymptotics ∼ rd−1 if the rotational average of the squared modulus of the Fourier transform of the set is O(ϰ−d−1). The asymptotics follow from Wiener’s Tauberian theorem.
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页码：751 / 758
页数：7
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