# 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 :
Preprints, Working Papers, ...

https://hal.inria.fr/hal-01379473
Contributor : Andreas Enge <>
Submitted on : Tuesday, October 11, 2016 - 3:33:57 PM
Last modification on : Thursday, August 22, 2019 - 2:02:39 PM

### Identifiers

• HAL Id : hal-01379473, version 1
• ARXIV : 1609.09153

### Citation

Henri Cohen, Frank Thorne. On $D_\ell$ extensions of odd prime degree $\ell$. 2016. ⟨hal-01379473⟩

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