# Dirichlet series associated to quartic fields with given cubic resolvent

1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Let $k$ 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 resolvent field is isomorphic to $k$. Our work is a sequel to an unpublished preprint of Cohen, Diaz y Diaz, and Olivier, and we include complete proofs of their results so as not to rely on unpublished work. This is a companion to a previous paper where we compute the Dirichlet series associated to cubic fields having a given quadratic resolvent.
Type de document :
Article dans une revue
Research in Number Theory, SpringerOpen, 2016, 2 (29), pp.1-40. <10.1007/s40993-015-0001-y>

https://hal.inria.fr/hal-00854664
Contributeur : Andreas Enge <>
Soumis le : mardi 27 août 2013 - 17:49:12
Dernière modification le : mercredi 22 février 2017 - 01:06:32

### Citation

Henri Cohen, Frank Thorne. Dirichlet series associated to quartic fields with given cubic resolvent. Research in Number Theory, SpringerOpen, 2016, 2 (29), pp.1-40. <10.1007/s40993-015-0001-y>. <hal-00854664>

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