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Weak Arithmetic Equivalence

Published online by Cambridge University Press:  20 November 2018

Guillermo Mantilla-Soler
Guillermo Mantilla-Soler*
Affiliation:
Departamento de Matemáticas, Universidad de los Andes, Carrera 1 N. 18A-10, Bogotá, Colombia. e-mail: g.mantilla691@uniandes.edu.co
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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

Keywords

11R0411R42artihmeticaly equivalent number fieldsroot numbers

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 1 , 01 March 2015 , pp. 115 - 127
Copyright
Copyright © Canadian Mathematical Society 2015

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