On the asymptotics of elementary-abelian extensions of local and global function fields

<p>We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. For local and rational function fields, we also give precise formulae for the number of elementary-abelian extensions with a fixed discriminant divisor, which describe a local-global principle.</p>