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arXiv · 1309.2025

The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields

Manjul Bhargava·Piper Harron
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Abstract

For $n=3$, 4, and 5, we prove that, when $S_n$-number fields of degree $n$ are ordered by their absolute discriminants, the lattice shapes of the rings of integers in these fields become equidistributed in the space of lattices.

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Manjul Bhargava, Piper Harron. 2013-09-09. The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields. https://doi.org/10.1112/s0010437x16007260

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