most citedCounting Cubic Extensions with given Quadratic Resolvent

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math.NT2013★ 1 cited

Dirichlet series associated to quartic fields with given resolvent

Henri Cohen, Frank Thorne

Let be a cubic field. We give an explicit formula for the Dirichlet series $\sum_K|\Disc(K)|^{-s}$, where the sum is over isomorphism classes of all quartic fields whose cubic…

math.NT2010★ 23 cited

Counting Cubic Extensions with given Quadratic Resolvent

Henri Cohen, Anna Morra

Given a number field and a quadratic extension , we give an explicit asymptotic formula for the number of isomorphism classes of cubic extensions of whose Galois closu…