The number of extensions of a number field with fixed degree and bounded discriminant

Details The number of extensions of a number field with fixed degree and bounded discriminant The number of extensions of a number field with fixed degree and bounded discriminant

2003-09-08

arxiv.org/abs/math/0309153v1

Mathematics

Number Theory

Scientific paper

We give an upper bound on the number of extensions of a fixed number field of
prescribed degree and discriminant less than 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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