C. Snyder

Imaginary quadratic fields with Cl2(k)≃(2,2,2)

Abstract We characterize those imaginary quadratic number fields, k, with 2-class group of type (2,2,2) and with the 2-rank of the class group of its Hilbert 2-class field equal to 2. We then compute the length of the 2-class field tower of k.

A concept of Bernoulli numbers in algebraic function fields (II)

As a continuation of our previous article [6], we consider a concept of Bernoulli numbers in an abstract algebraic function field in one variable of characteristic zero with respect to an abstract differential. We establish that certain Kummer-type congruences are essentially dependent only on the differential and not upon any particular basis for the differential. Applications of this theory are then given.

ELEMENTS OF ORDER FOUR IN THE NARROW CLASS GROUP OF REAL QUADRATIC FIELDS

Using the elements of order four in the narrow ideal class group, we construct generators of the maximal elementary

On the construction of the regular hendecagon by marked ruler and compass

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Real Quadratic Fields with Abelian 2-Class Field Tower

-class group of real quadratic number fields with even discriminant which is a sum of two squares and with fundamental unit of positive norm. We then give a characterization of when two of these generators are equal in the narrow sense in terms of norms of Gaussian integers.

Real Quadratic Number Fields with 2-Class Group of Type (2,2).

We prove that the regular hendecagon (11-gon) is constructible by marked ruler and compass.