User talk:RobHar/Sandbox

Current Project: Rewrite of Discriminant of an algebraic number field.

Other additions to discriminant

Perhaps add results on asymptotics of discriminant. For example, for cubic fields, the number of (isomorphism classes) of cubic fields with discriminant between 0 and X is asymptotic to

${\frac {X}{12\zeta (3)}}$

and between -X and 0 is asymptotic to

${\frac {X}{4\zeta (3)}}$

Both results due to Davenport-Heilbronn On the density of discriminants of cubic fields, II. For quartic rings, Bhargava The density of discriminants of quartic rings and fields, Cohen, Diaz y Diaz, and Olivier Enumerating Quartic Dihedral extensions of Q, Baily On the density of discriminants of Quartic fields, ? Wong Automorphic Forms on GL(2) and the rank of class groups. —Preceding unsigned comment added by RobHar (talk • contribs) 01:59, 15 November 2007 (UTC)