User talk:RobHar/Sandbox

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

[edit] 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)