EuDML | Browse

Page 1

Displaying 1 – 14 of 14

The class number one problem for some non-abelian normal CM-fields of degree $24$

F. Lemmermeyer, S. Louboutin, R. Okazaki (1999)

Journal de théorie des nombres de Bordeaux

We determine all the non-abelian normal CM-fields of degree 24 with class number one, provided that the Galois group of their maximal real subfields is isomorphic to $𝒜_{4}$ , the alternating group of degree $4$ and order $12$ . There are two such fields with Galois group $𝒜_{4} \times 𝒞_{2}$ (see Theorem 14) and at most one with Galois group SL $_{2} (𝔽_{3})$ (see Theorem 18); if the generalized Riemann hypothesis is true, then this last field has class number $1$ .

The class number one problem for the dihedral and dicyclic CM-fields

Stéphane Louboutin (1999)

Colloquium Mathematicae

We recall the determination of all the dihedral CM-fields with relative class number one, and prove that dicyclic CM-fields have relative class numbers greater than one.

Displaying 1 – 14 of 14

The class number one problem for some non-abelian normal CM-fields of degree $24$

The class number one problem for the dihedral and dicyclic CM-fields

The class number one problem for the non-abelian normal CM-fields of degree 16

The class number one problem for the non-abelian normal CM-fields of degree 24 and 40

The class number one problem for the non-normal sextic CM-fields. Part 2

The construction of unramified abelian cubic extensions of a quadratic field

The Hasse norm principle in non-abelian extensions.

The non-abelian normal CM-fields of degree 36 with class number one

The polylogarithm in the field of two irreducible quintics.

The $S_{5}$ extensions of degree 6 with minimum discriminant.

The Stufe of Number Fields.

The totally real $A_{5}$ extension of degree 6 with minimum discriminant.

The totally real $A_{6}$ extension of degree 6 with minimum discriminant.

Truncated units in the algebraic number field $Q (w)$ , where $w^{n} = a + b w$ , $n \geq 3$

Currently displaying 1 – 14 of 14