The Shape of cyclic number fields

2019/12/15 by Wilmar Bolaños, Bolaños, Wilmar, Guillermo Mantilla-Soler +1
Computer Science · Engineering · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1912.07054

openalex publication_date 2019/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let m>1 and \mathfrakd ≠ 0 be integers such that v_p(\mathfrakd) ≠ m for any prime p. We construct a matrix A(\mathfrakd) of size (m-1) × (m-1) depending on only of \mathfrakd with the following property: For any tame ℤ/mℤ-number field K of discriminant \mathfrakd the matrix A(\mathfrakd) represents the Gram matrix of the integral trace zero form of K. In particular, we have that the integral trace zero form of tame cyclic number fields is determined by the degree and discriminant of the field. Furthermore, if in addition to the above hypotheses, we consider real number fields, then the shape is also determined by the degree and the discriminant

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