二元情况下的淬火完美点阵

Pub Date : 2024-03-20 DOI:10.1016/j.jnt.2024.02.009

Erik Bahnson, Mark McConnell, Kyrie McIntosh

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引用次数: 0

摘要

文献[14]介绍了一种计算 SLn 赫克算子的新算法。该算法使用经过调和的完美点阵，即某些点阵对和二次方程式。它们概括了 Voronoi 完美网格[17]。本文是描述钢化完全网格特征的第一步。我们获得了平面内的完整分类，其中赫克算子是针对 SL2(Z) 及其算术子群的。这些结果取决于虚二次数域中阶的类场理论。

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Tempered perfect lattices in the binary case

A new algorithm for computing Hecke operators for ${SL}_{n}$ was introduced in [14]. The algorithm uses tempered perfect lattices, which are certain pairs of lattices together with a quadratic form. These generalize the perfect lattices of Voronoi [17]. The present paper is the first step in characterizing tempered perfect lattices. We obtain a complete classification in the plane, where the Hecke operators are for ${SL}_{2} (Z)$ and its arithmetic subgroups. The results depend on the class field theory of orders in imaginary quadratic number fields.

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