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

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  15 April 2016

Manjul Bhargava  and
Piper Harron
Manjul Bhargava
Affiliation:
Department of Mathematics, Fine Hall, Princeton University, Princeton, NJ 08544, USA email [email protected]
Piper Harron
Affiliation:
Honolulu, HI, USA email [email protected]
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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.

Keywords

equidistributionlattice shapesnumber fields

MSC classification

Primary: 11R04: Algebraic numbers; rings of algebraic integers
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 6 , June 2016 , pp. 1111 - 1120
Copyright
© The Authors 2016 

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