论文标题
$ s_n $ -number字段数量的渐近学启发式方法
Heuristics for the asymptotics of the number of $S_n$-number fields
论文作者
论文摘要
我们给出了一个启发式论点，支持Bhargava对$ s_n $ -number领域的渐近数的猜想。然后，在情况下，我们对$ n = 3 $进行了严格的论点，提供了Davenport-Heilbronn定理的新基本证明。我们的基本方法是计算$ s_n $ fields的高度小元素，同时仔细跟踪其产生的单基因戒指的索引。
We give a heuristic argument supporting conjectures of Bhargava on the asymptotics of the number of $S_n$-number fields having bounded discriminant. We then make our arguments rigorous in the case $n=3$ giving a new elementary proof of the Davenport-Heilbronn theorem. Our basic method is to count elements of small height in $S_n$-fields while carefully keeping track of the index of the monogenic ring that they generate.
