球设计与欧氏格的高
Spherical Designs and Heights of Euclidean Lattices
摘要：
我们研究了球面设计理论与格点高度函数极值问题之间的联系。更确切地说，我们表明，一个满秩的n维欧几里德晶格，其中所有层举行的球形2-设计，实现了一个固定点的高度函数，这是定义为在0的频谱zeta函数的相关平坦环面的一阶导数。此外，为了找出这种2-设计属性持有的格，一种策略，它利用了θ函数与球面系数，被视为元素的一些空间的模形式。显式计算的尺寸高达7，进行与帕里/GP和岩浆，报告。
英文摘要：
We study the connection between the theory of spherical designs and the question of extrema of the height function of lattices. More precisely, we show that a full-rank n-dimensional Euclidean lattice, all layers of which hold a spherical 2-design, realises a stationary point for the height function, which is defined as the first derivative at 0 of the spectral zeta function of the associated flat torus. Moreover, in order to find out the lattices for which this 2-design property holds, a strategy is described which makes use of theta functions with spherical coefficients, viewed as elements of some space of modular forms. Explicit computations in dimension up to 7, performed with Pari/GP and Magma, are reported.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
