论文标题
在晶格扩展方面
On lattice extensions
论文作者
论文摘要
如果$ l $等于$λ$与$ l $的子空间相交，则据说晶格$λ$是较小排名的Sublattice $ l $。本文的目的是对晶格扩展的几何形状进行系统研究。我们首先证明给定晶格的小确定扩展存在，然后查看连续的最小值和覆盖半径。为此，我们调查了保留给定晶格的连续最小值的扩展（在环境晶格中），以及保留覆盖半径的扩展。我们还展示了平面晶格深孔的一些有趣的算术特性。
A lattice $Λ$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $Λ$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry of lattice extensions. We start by proving the existence of a small-determinant extension of a given lattice, and then look at successive minima and covering radius. To this end, we investigate extensions (within an ambient lattice) preserving the successive minima of the given lattice, as well as extensions preserving the covering radius. We also exhibit some interesting arithmetic properties of deep holes of planar lattices.
