%0 Journal Article %A Manjul Bhargava %T The density of discriminants of quartic rings and fields %J Annals of mathematics %D 2005 %P 1031-1063 %V 162 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.162.1031/ %R 10.4007/annals.2005.162.1031 %G en %F 10_4007_annals_2005_162_1031