A fascinating tale of mayhem, mystery, and mathematics. Attached to each degree n number field is a rank n -- 1 lattice called its shape. This thesis shows that the shapes of Sn-number fields (of degree n = 3,4, or 5) become equidistributed as the absolute discriminant of the number field goes to infinity. The result for n = 3 is due to David Terr. Here, we provide a unified proof for n = 3, 4, and 5 based on the parametrizations of low rank rings due to Bhargava and Delone--Faddeev. We do not assume any of those words make any kind of sense, though we do make certain assumptions about how much time the reader has on her hands and what kind of sense of humor she has.
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机译:令人着迷的混乱,神秘和数学故事。每个n度数字段都附加一个n-1级格,称为其形状。该论文表明,随着次数场的绝对判别变为无穷大,Sn次数场(n = 3,4或5)的形状变得均匀分布。 n = 3的结果归因于David Terr。在此,我们根据由于Bhargava和Delone-Faddeev引起的低秩环的参数化,为n = 3、4和5提供了统一的证明。尽管我们确实对读者有多长时间以及她拥有什么样的幽默感做出了某些假设,但我们不认为这些词具有任何意义。
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