# On $D_\ell$ extensions of odd prime degree $\ell$

2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Generalizing the work of A. Morra and the authors, we give explicit formulas for the Dirichlet series generating function of $D_ℓ$-extensions of odd prime degree $ℓ$ with given quadratic resolvent. Over the course of our proof, we explain connections between our formulas and the Ankeny-Artin-Chowla conjecture, the Ohno-Nakagawa relation for binary cubic forms, and other topics.
Document type :
Journal articles

https://hal.inria.fr/hal-01379473
Contributor : Andreas Enge Connect in order to contact the contributor
Submitted on : Tuesday, October 11, 2016 - 3:33:57 PM
Last modification on : Wednesday, October 20, 2021 - 12:17:25 AM

### Citation

Henri Cohen, Frank Thorne. On $D_\ell$ extensions of odd prime degree $\ell$. Proceedings of the London Mathematical Society, London Mathematical Society, 2020, 121 (5), pp.1171-1206. ⟨10.1112/plms.12339⟩. ⟨hal-01379473⟩

Record views