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

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.

12 pages

References in corpus (1)

• On the number of cubic orders of bounded discriminant having automorphism group $C_3$, and related problems

Cited by in corpus (3)

• The shape of cubic fields
• Equidistribution of shapes of complex cubic fields of fixed quadratic resolvent
• Equidistribution of bounded torsion CM points