Dirichlet series associated to quartic fields with given cubic resolvent
COHEN, Henri
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
COHEN, Henri
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
< Réduire
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Langue
en
Article de revue
Ce document a été publié dans
Research in Number Theory. 2016, vol. 2, n° 29, p. 1-40
Springer
Résumé en anglais
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 ...Lire la suite >
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 Our work is a sequel to an unpublished preprint of Cohen, Diaz y Diaz, and Olivier, and we include complete proofs of their results so as not to rely on unpublished work.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.< Réduire
Projet Européen
Algorithmic Number Theory in Computer Science
Origine
Importé de halUnités de recherche