Arithmetic equivalence under isoclinism

Abstract

Two algebraic number fields are called arithmetically equivalent if the Dedekind zeta functions of the fields coincide. We show that if a G-extension contains non-conjugate arithmetically equivalent fields and there is an injection from G to another group H inducing an isoclinism between G and H, then there are non-conjugate arithmetically equivalent fields inside an H-extension.

KEYWORDS:

• Arithmetically equivalent fields
• Dedekind zeta function
• Gassmann equivalence
• isoclinism

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 11R42
• 20D60
• 20E45

Additional information

Funding

This work was supported by JSPS KAKENHI Grant Number 20K03521.