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arXiv · 1310.2990

Weak arithmetic equivalence

Guillermo Mantilla-Soler
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Abstract

Inspired by the invariant of a number field given by its zeta function, we define the notion of {\it weak arithmetic equivalence}, and show that under certain ramification hypothesis, 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 weak arithmetic equivalence.

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Guillermo Mantilla-Soler. 2014-09-12. Weak arithmetic equivalence. https://doi.org/10.4153/cmb-2014-036-7

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