极大θ函数--类Madelung格点能量的泛最优性
Maximal Theta Functions -- Universal Optimality of the Hexagonal Lattice for Madelung-Like Lattice Energies
摘要：
本文给出了两类格θ函数，它们与Montgomery在[H.~]中研究的格θ函数族相对应.蒙哥马利最小θ函数。\textit{Glasgow Mathematical Journal}，30（1）：75- 85，1988]。所研究的θ函数是Jacobi θ 2和θ 4函数的推广。与Montgomery的结果相反，我们证明了在格子中，六角格子是两个θ函数族的唯一极大化者。作为直接的结果，我们得到了一个新的普遍最优性的结果之间的二维交替充电的晶格和晶格移动的中心，其单位电池的六角晶格。
英文摘要：
We present two families of lattice theta functions accompanying the family of lattice theta functions studied by Montgomery in [H.~Montgomery. Minimal theta functions. \textit{Glasgow Mathematical Journal}, 30(1):75--85, 1988]. The studied theta functions are generalizations of the Jacobi theta-2 and theta-4 functions. Contrary to Montgomery's result, we show that, among lattices, the hexagonal lattice is the unique maximizer of both families of theta functions. As an immediate consequence, we obtain a new universal optimality result for the hexagonal lattice among two-dimensional alternating charged lattices and lattices shifted by the center of their unit cell.
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