The number of extensions of a number field with fixed degree and bounded discriminant
Annals of Mathematics2006Vol. 163(2), pp. 723–741
Citations Over TimeTop 10% of 2006 papers
Abstract
We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant X; these bounds improve on work of Schmidt. We also prove various related results, such as lower bounds for the number of extensions and upper bounds for Galois extensions.
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