Finite evaluation of the class number of quadratic number fields

Ternary quadratic forms over number fields with small class number

We enumerate all positive definite ternary quadratic forms over number fields with class number at most 2. This is done by constructing all definite quaternion orders of type number at most 2 over number fields. Finally, we list all definite quaternion orders of ideal class number 1 or 2.

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 Divisibility of the Class Number of Quadratic Fields

The 4-class Group of Real Quadratic Number Fields

In this paper we give an elementary proof of results on the structure of 4-class groups of real quadratic number fields originally due to A. Scholz. In a second (and independent) section we strengthen C. Maire’s result that the 2-class field tower of a real quadratic number field is infinite if its ideal class group has 4-rank ≥ 4, using a technique due to F. Hajir.

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 ...