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

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.
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Contributor : Andreas Enge Connect in order to contact the contributor
Submitted on : Tuesday, October 11, 2016 - 3:33:57 PM
Last modification on : Friday, November 18, 2022 - 9:25:38 AM

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



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