论文标题
整数环的格格在数量3,4和5的数字字段中的等式分布
The Equidistribution of Grids of Rings of Integers in Number Fields of Degrees 3,4 and 5
论文作者
论文摘要
M. Bhargava和P. Harron表明，以$ n = 3,4,5 $，$ s_n $ number $ n $的整数环形状的形状在形状的空间中等于界面。我们将网格与每个数字字段相对应，而不是形状，该网格保留了更多数字字段的数据。网格的空间是形状空间上的纤维束。我们通过证明$ s_n $ -number田地的整数环的网格在网格空间中等分。
It was shown by M. Bhargava and P. Harron that for $n=3,4,5$, the shapes of rings of integers of $S_n$-number fields of degree $n$ become equidistributed in the space of shapes when the fields are ordered by discriminant. Instead of shapes, we correspond grids to each number field, which preserve more of the number fields' data. The space of grids is a fiber bundle over the space of shapes. We strengthen Bhargava-Harron's result by proving that the grids of rings of integers of $S_n$-number fields become equidistributed in the space of grids.
