Two number fields are **arithmetically equivalent** if they have the same Dedekind $\zeta$-functions. Arithmetically equivalent fields share many invariants, such as their degrees, signatures, discriminants, and Galois groups. For a given field, the existence of an arithmetically equivalent sibling depends only on the Galois group.

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- Last edited by John Jones on 2020-10-11 16:29:02

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- 2020-10-11 16:29:02 by John Jones (Reviewed)
- 2018-07-07 21:49:26 by Kiran S. Kedlaya (Reviewed)

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