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Journal Articles Proceedings of the London Mathematical Society Year : 2020

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.

Dates and versions

hal-01379473 , version 1 (11-10-2016)

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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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