Geodesic
Weak Arithmetic Equivalence
Canadian mathematical bulletin, Tome 58 (2015) no. 1, pp. 115-127

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DOI

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
DOI : 10.4153/CMB-2014-036-7
Mots-clés : 11R04, 11R42, artihmeticaly equivalent number fields, root numbers 
Mantilla-Soler, Guillermo. Weak Arithmetic Equivalence. Canadian mathematical bulletin, Tome 58 (2015) no. 1, pp. 115-127. doi: 10.4153/CMB-2014-036-7
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     author = {Mantilla-Soler, Guillermo},
     title = {Weak {Arithmetic} {Equivalence}},
     journal = {Canadian mathematical bulletin},
     pages = {115--127},
     year = {2015},
     volume = {58},
     number = {1},
     doi = {10.4153/CMB-2014-036-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-036-7/}
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