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The Trace Form Over Cyclic Number Fields

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  14 April 2020

Wilmar Bolaños  and
Guillermo Mantilla-Soler
Wilmar Bolaños
Affiliation:
Department of Mathematics, Universidad de los Andes, Bogotá, Colombia e-mail: wr.bolanos915@uniandes.edu.co
Guillermo Mantilla-Soler*
Affiliation:
Guillermo Mantilla-Soler, Department of Mathematics, Universidad Konrad Lorenz, Bogotá, Colombia, and Department of Mathematics and Systems Analysis, Aalto University, Espoo, Finland
*
e-mail: gmantelia@gmail.com
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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.

Keywords

Cyclic number fieldstrace form

MSC classification

Primary: 11R04: Algebraic numbers; rings of algebraic integers
Secondary: 11R18: Cyclotomic extensions 11R29: Class numbers, class groups, discriminants 11R32: Galois theory
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 4 , August 2021 , pp. 947 - 969
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Copyright
© Canadian Mathematical Society 2020

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