On the Class Number of Relative Quadratic Fields

On the Divisibility of the Class Number of Quadratic Fields

On a Class Number Formula for Real Quadratic Number Fields

For an even Dirichlet character , we obtain a formula for L(1;) in terms of a sum of Dirichlet L-series evaluated at s = 2 and s = 3 and a rapidly convergent numerical series involving the central binomial coeecients. We then derive a class number formula for real quadratic number elds by taking L(s;) to be the quadratic L-series associated with these elds.

On the Class Number of Real Quadratic Fields.

* Aided by a grant from the Swiss National Foundation for Scientific Research. t Aided by a grant from the National Foundation. t The small band appearing on the dense side of b2b5 in Fig. 2 contains only 0.2% of the phages; it is not due to an error in collecting the drops, for if the phages are centrifuged again in the density gradient, these phages appear at the same density; however, after ...

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.

CM-fields with relative class number one

We will show that the normal CM-fields with relative class number one are of degrees ≤ 216. Moreover, if we assume the Generalized Riemann Hypothesis, then the normal CM-fields with relative class number one are of degrees ≤ 96, and the CM-fields with class number one are of degrees ≤ 104. By many authors all normal CM-fields of degrees ≤ 96 with class number one are known except for the possib...