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The shape of $\mathbb{Z}/\ell\mathbb{Z}$-number fields

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  • Additional Information
    • Publication Date:
      2013
    • Collection:
      ArXiv.org (Cornell University Library)
    • Abstract:
      Let $\ell$ be a prime and let $L/\mathbb{Q}$ be a Galois number field with Galois group isomorphic to $\mathbb{Z}/\ell\mathbb{Z}$. We show that the {\it shape} of $L$ is either $\frac{1}{2}\mathbb{A}_{\ell-1}$ or a fixed sub lattice depending only on $\ell$; such a dichotomy in the value of the shape only depends on the type of ramification of $L$. This work is motivated by a result of Bhargava and Shnidman, and a previous work of the first named author, on the shape of $\mathbb{Z}/3\mathbb{Z}$ number fields. ; Comment: I have added, and clarified some proofs. A version of this paper will appear soon in the Ramanujan Journal
    • Relation:
      http://arxiv.org/abs/1311.0387
    • Accession Number:
      10.1007/s11139-015-9744-2
    • Online Access:
      https://doi.org/10.1007/s11139-015-9744-2
      http://arxiv.org/abs/1311.0387
    • Accession Number:
      edsbas.C8672632