A Minimum Problem for the Epstein Zeta-Function
A Minimum Problem for the Epstein Zeta-Function
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DOI：
10.1017/s2040618500035668
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发表时间：
1953-12
期刊：
影响因子：
--
通讯作者：
R. Rankin
中科院分区：
文献类型：
--
作者：
R. Rankin
在D. G.肯德尔和作者†的点的数量的一个格子在于一个随机的圆的平均值的方差出现作为一个常数倍的价值爱泼斯坦zeta函数Z（s）与晶格，采取在点s=。由于与最密堆积和覆盖问题的联系，似乎Z（）的最小值在六方格子中是可能达到的，本文的目的是证明这一点，并将结果推广到变量s的其他真实的值。
In some recent work by D. G. Kendall and the author † on the number of points of a lattice which lie in a random circle the mean value of the variance emerged as a constant multiple of the value of the Epstein zeta-function Z(s) associated with the lattice, taken at the point s=. Because of the connexion with the problems of closest packing and covering it seemed likely that the minimum value of Z() would be attained for the hexagonal lattice; it is the purpose of this paper to prove this and to extend the result to other real values of the variable s.