论文标题
最大theta函数 - 六角形晶格的通用最优性
Maximal Theta Functions -- Universal Optimality of the Hexagonal Lattice for Madelung-Like Lattice Energies
论文作者
论文摘要
我们介绍了由蒙哥马利（H.最小的theta功能。 \ textit {Glasgow Mathematical Journal}，30（1）：75--85，1988]。研究的theta函数是jacobi theta-2和theta-4函数的概括。与蒙哥马利的结果相反，我们表明，在晶格中，六角形晶格是theta功能的两个家族的独特最大化器。直接的结果，我们在二维交替的带电晶格和晶格中的六边形晶格中获得了新的通用最优结果，并从其单位电池的中心移动。
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.
