Squarefree values of polynomial discriminants II

Abstract

We determine the density of integral binary forms of given degree that have squarefree discriminant, proving for the first time that the lower density is positive. Furthermore, we determine the density of integral binary forms that cut out maximal orders in number fields. The latter proves, in particular, an ‘arithmetic Bertini theorem’ conjectured by Poonen for ${\mathbb {P}}^1_{\mathbb {Z}}$ .

Keywords

• 11N35
• 11C08
• 11R09
• 11H06