Geodesic
Arithmetically equivalent fields in a Galois extension with Frobenius Galois group of 2-power degree
Canadian mathematical bulletin, Tome 66 (2023) no. 2, pp. 380-394

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DOI

Let $F_{2^n}$ be the Frobenius group of degree $2^n$ and of order $2^n ( 2^n-1)$ with $n \ge 4$. We show that if $K/\mathbb {Q} $ is a Galois extension whose Galois group is isomorphic to $F_{2^n}$, then there are $\dfrac {2^{n-1} +(-1)^n }{3}$ intermediate fields of $K/\mathbb {Q} $ of degree $4 (2^n-1)$ such that they are not conjugate over $\mathbb {Q}$ but arithmetically equivalent over $\mathbb {Q}$. We also give an explicit method to construct these arithmetically equivalent fields.
DOI : 10.4153/S0008439522000388
Mots-clés : Dedekind zeta function, arithmetically equivalent fields, Frobenius group, inverse Galois problem 
Kida, Masanari. Arithmetically equivalent fields in a Galois extension with Frobenius Galois group of 2-power degree. Canadian mathematical bulletin, Tome 66 (2023) no. 2, pp. 380-394. doi: 10.4153/S0008439522000388
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     title = {Arithmetically equivalent fields in a {Galois} extension with {Frobenius} {Galois} group of 2-power degree},
     journal = {Canadian mathematical bulletin},
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     year = {2023},
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     doi = {10.4153/S0008439522000388},
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