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Weak Arithmetic Equivalence

Published online by Cambridge University Press:  20 November 2018

Guillermo Mantilla-Soler*
Affiliation:
Departamento de Matemáticas, Universidad de los Andes, Carrera 1 N. 18A-10, Bogotá, Colombia. e-mail: [email protected]
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Abstract

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Inspired by the invariant of a number field given by its zeta function, we define the notion of weak arithmetic equivalence and show that under certain ramification hypotheses this equivalence determines the local root numbers of the number field. This is analogous to a result of Rohrlich on the local root numbers of a rational elliptic curve. Additionally, we prove that for tame non-totally real number fields, the integral trace form is invariant under arithmetic equivalence

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2015

References

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