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

Published online by Cambridge University Press:  15 April 2016

Manjul Bhargava
Affiliation:
Department of Mathematics, Fine Hall, Princeton University, Princeton, NJ 08544, USA email bhargava@math.princeton.edu
Piper Harron
Affiliation:
Honolulu, HI, USA email paharron@gmail.com
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Abstract

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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.

Type
Research Article
Copyright
© The Authors 2016 

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