On mod logarithms and .
A Note on the Growth of Davenport's constant.
A generalization of a theorem of Minkowski
Remarks on normal bases
We prove that any Galois extension of a commutative ring with a normal basis and abelian Galois group of odd order has a self-dual normal basis. We apply this result to get a very simple proof of nonexistence of normal bases for certain extensions which are of interest in number theory.
On the relationship between hyperbolic and cone-hyperbolic structures in metric spaces
We give necessary and sufficient conditions for topological hyperbolicity of a homeomorphism of a metric space, restricted to a given compact invariant set. These conditions are related to the existence of an appropriate finite covering of this set and a corresponding cone-hyperbolic graph-directed iterated function system.
Galois module structure of units in real biquadratic number fields
Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields
We investigate as Galois module the unit group of biquadratic extensions of number fields. The -rank of the first cohomology group of units of is computed for general . For imaginary quadratic we determine a large portion of the cases (including all unramified ) where the index takes its maximum value , where are units mod torsion of and are units mod torsion of one of the 3 quadratic subfields of .
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