Counting Cubic Extensions with given Quadratic Resolvent
COHEN, Henri
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
MORRA, Anna
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
COHEN, Henri
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
MORRA, Anna
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Language
en
Article de revue
This item was published in
Journal of Algebra. 2011-01-01, vol. 325, p. 461-478
Elsevier
English Abstract
Given a number field $k$ and a quadratic extension $K_2$, we give an explicit asymptotic formula for the number of isomorphism classes of cubic extensions of $k$ whose Galois closure contains $K_2$ as quadratic subextension, ...Read more >
Given a number field $k$ and a quadratic extension $K_2$, we give an explicit asymptotic formula for the number of isomorphism classes of cubic extensions of $k$ whose Galois closure contains $K_2$ as quadratic subextension, ordered by the norm of their relative discriminant ideal. The main tool is Kummer theory. We also study in detail the error term of the asymptotics and show that it is $O(X^{\alpha})$, for an explicit $\alpha<1$.Read less <
Origin
Hal imported