On the quadratic subfield of a ${\bf Z}\sb 2$-extension of an imaginary quadratic number field

On 2-class field towers of imaginary quadratic number fields

For a number field k, let k1 denote its Hilbert 2-class field, and put k2 = (k1)1. We will determine all imaginary quadratic number fields k such that G = Gal(k2/k) is abelian or metacyclic, and we will give G in terms of generators and relations.

L - Functions and Class Numbers of Imaginary Quadratic Fields and of Quadratic Extensions of an Imaginary Quadratic Field

Starting from the analytic class number formula involving its Lfunction, we first give an expression for the class number of an imaginary quadratic field which, in the case of large discriminants, provides us with a much more powerful numerical technique than that of counting the number of reduced definite positive binary quadratic forms, as has been used by Buell in order to compute his class ...

The Stickelberger element of an imaginary quadratic field

On 2-class Field Towers of Some Imaginary Quadratic Number Fields

We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2, 2, 2) whose Hilbert 2-class fields are finite.

On the Equivariant Tamagawa Number Conjecture for Abelian Extensions of a Quadratic Imaginary Field

Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extension of k and let K be a subextension of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h(Spec(L)),Z[Gal(L/K)]). 2000 Mathematics Subject Classification: 11G40, 11R23, 11R33, 11R65