Weak arithmetic equivalence
Number Theory
2019-08-15 v2
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.
Keywords
Cite
@article{arxiv.1310.2990,
title = {Weak arithmetic equivalence},
author = {Guillermo Mantilla-Soler},
journal= {arXiv preprint arXiv:1310.2990},
year = {2019}
}
Comments
I've changed some proofs and I've provided more examples. I have also added a new lemma that resolves some previously open questions in a former version of the paper