On lattice points in n-dimensional star bodies I. Existence theorems
On lattice points in n-dimensional star bodies I. Existence theorems
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关于n维星体中的格点Ⅰ.存在定理
DOI：
10.1098/rspa.1946.0072
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发表时间：
1946
期刊：
影响因子：
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通讯作者：
L. Mordell
中科院分区：
文献类型：
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作者：
K. Mahler;L. Mordell
设F（X）= F（x1，...，xn）是X的连续非负函数，满足F（tX）=|不|F（X）对所有真实的数t.由F（X）∈ 1定义的n维欧氏空间Rn中的集合K称为星星体。本文研究了Rn中具有最小行列式且除（0，…，0)在K。他调查了有多少点，这种格在于，或接近，边界的K，并认为详细的情况下，当K承认一个无限组的线性变换本身。
Let F(X) = F(x1,..., xn) be a continuous non-negative function of X satisfying F(tX) = |t|F(X) for all real numbers t. The set K in n-dimensional Euclidean space Rn defined by F(X)⩽ 1 is called a star body. The author studies the lattices Λ in Rn which are of minimum determinant and have no point except (0, ..., 0) inside K. He investigates how many points of such lattices lie on, or near to, the boundary of K, and considers in detail the case when K admits an infinite group of linear transformations into itself.