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Note on the congruence of Ankeny-Artin-Chowla type modulo p²

Stanislav Jakubec (1998)

Acta Arithmetica

The results of [2] on the congruence of Ankeny-Artin-Chowla type modulo p² for real subfields of ( ζ p ) of a prime degree l is simplified. This is done on the basis of a congruence for the Gauss period (Theorem 1). The results are applied for the quadratic field ℚ(√p), p ≡ 5 (mod 8) (Corollary 1).

Note on the Hilbert 2-class field tower

Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini (2022)

Mathematica Bohemica

Let k be a number field with a 2-class group isomorphic to the Klein four-group. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields 𝕜 = ( d , - 1 ) , which leads to a correction of some parts in the main results of A. Azizi and A. Zekhini (2020).

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