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Metaplectic covers of G L n and the Gauss-Schering lemma

Richard Hill (2001)

Journal de théorie des nombres de Bordeaux

The Gauss-Schering Lemma is a classical formula for the Legendre symbol commonly used in elementary proofs of the quadratic reciprocity law. In this paper we show how the Gauss Schering Lemma may be generalized to give a formula for a 2 -cocycle corresponding to a higher metaplectic extension of GL n / k for any global field k . In the case that k has positive characteristic, our formula gives a complete construction of the metaplectic group and consequently an independent proof of the power reciprocity...

Monogénéité de l'anneau des entiers de certains corps de classes de rayon

Vincent Fleckinger (1988)

Annales de l'institut Fourier

Soient k une extension quadratique imaginaire de Q et A son anneau des entiers. Lorsque 3 est décomposé dans k , nous démontrons que les anneaux d’entiers de certains corps de classe de rayon de k sont monogènes sur l’anneau des entiers du corps de classes de rayon 3. Des générateurs de “monogénéite” sont obtenus a l’aide de fonctions elliptiques qui paramétrisent un modèle de Deuring de la courbe elliptique associée au réseau A .

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 = ℚ ( d , - 1 ) , which leads to a correction of some parts in the main results of A. Azizi and A. Zekhini (2020).

On 2 -class field towers of imaginary quadratic number fields

Franz Lemmermeyer (1994)

Journal de théorie des nombres de Bordeaux

For a number field k , let k 1 denote its Hilbert 2 -class field, and put k 2 = ( k 1 ) 1 . We will determine all imaginary quadratic number fields k such that G = G a l ( k 2 / k ) is abelian or metacyclic, and we will give G in terms of generators and relations.

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