Dirichlet Series Associated to Quartic Fields with given Resolvent
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چکیده
Let k be a cubic field. We give an explicit formula for the Dirichlet series P K |Disc(K)| −s, where the sum is over isomorphism classes of all quartic fields whose cubic resolvent field is isomorphic to k. Our work is a sequel to the unpublished preprint [11] whose results have been summarized in [6], so we include complete proofs so as not to rely on unpublished work. This is a companion paper to [13] where we compute the Dirichlet series associated to cubic fields having a given quadratic resolvent.
منابع مشابه
Dirichlet series associated to quartic fields with given cubic resolvent
Let k be a cubic field. We give an explicit formula for the Dirichlet series ∑ K |Disc(K)|−s, where the sum is over isomorphism classes of all quartic fields whose cubic resolvent field is isomorphic to k. Our work is a sequel to the unpublished preprint [12] whose results have been summarized in [7], so we include complete proofs so as not to rely on unpublished work. This is a companion paper...
متن کاملAppendix To: Dirichlet Series Associated to Quartic Fields with given Resolvent
This is an appendix to our paper [1], where we give an explicit formula for the Dirichlet series ∑ K |Disc(K)|−s, where the sum is over isomorphism classes of all quartic fields whose cubic resolvent field is isomorphic to k. In the present note, we give a complete proof of a theorem enumerating splitting types of certain number fields, which was stated in [1] without a complete proof. The deta...
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تاریخ انتشار 2013