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

  • Manjul Bhargava (a1) and Piper Harron (a2)
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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© The Authors 2016 
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

M. Bhargava , Higher composition laws III: the parametrization of quartic rings, Ann. of Math. (2) 159 (2004), 1329–1360.
M. Bhargava , The density of discriminants of quartic rings and fields, Ann. of Math. (2) 162 (2005), 1031–1063.
M. Bhargava , Higher composition laws IV: the parametrization of quintic rings, Ann. of Math. (2) 167 (2008), 53–94.
M. Bhargava , The density of discriminants of quintic rings and fields, Ann. of Math. (2) 172 (2010), 1559–1591.
M. Bhargava and A. Shnidman , On the number of cubic orders of bounded discriminant having automorphism group C3 , and related problems, Algebra Number Theory 8 (2014), 53–88.
A. Borel and , Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485–535.
H. Davenport and H. Heilbronn , On the density of discriminants of cubic fields. II, Proc. R. Soc. Lond. Ser. A 322 (1971), 405–420.
T. Shintani , On Dirichlet series whose coefficients are class numbers of integral binary cubic forms, J. Math. Soc. Japan 24 (1972), 132–188.
D. Wright and A. Yukie , Prehomogeneous vector spaces and field extensions, Invent. Math. 110 (1992), 283–314.
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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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