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The trace form over cyclic number fields

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arxiv 1904.10080 v3 pith:IJY54IXW submitted 2019-04-22 math.NT

Wilmar Bolaños , Guillermo Mantilla-Soler This is my paper · ORCID
classification math.NT
keywords fieldscyclicnumbertracedegreediscriminantintegralarbitrary
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abstract

In the mid 80's Conner and Perlis showed that for cyclic number fields of prime degree $p$ the isometry class of integral trace is completely determined by the discriminant. Here we generalize their result to tame cyclic number fields of arbitrary degree. Furthermore, for such fields, we give an explicit description of a Gram matrix of the integral trace in terms of the discriminant of the field.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The shapes of Galois quartic fields

    math.NT 2019-08 accept novelty 7.0 of 10

    All Galois quartic fields have shapes that are orthorhombic for V4 groups (with regularized equidistribution) and tetragonal for C4 groups (with explicit per-shape counting asymptotics).

  2. An introduction to $\Gamma$-number fields

    math.NT 2019-08 reject novelty 6.0 of 10

    For Gamma-number fields, the spinor genus of the integral trace form is determined exactly by the discriminant and the signature.

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