354 research outputs found
Hilbert 90 for biquadratic extensions
Hilbert's Theorem 90 is a classical result in the theory of cyclic
extensions. The quadratic case of Hilbert 90, however, generalizes in noncyclic
directions as well. Informed by a poem of Richard Wilbur, the article explores
several generalizations, discerning connections among multiplicative groups of
fields, values of binary quadratic forms, a bit of module theory over group
rings, and even Galois cohomology.Comment: v2 (15 pages); followed Monthly style sheet and added additional
expositio
Kuroda's formula and arithmetic statistics
Kuroda's formula relates the class number of a multi-quadratic number field
to the class numbers of its quadratic subfields . A key component in
this formula is the unit group index . We study how behaves on average in
certain natural families of totally real biquadratic fields parametrized by
prime numbers
On the strongly ambiguous classes of some biquadratic number fields
We study the capitulation of ideal classes in an infinite family of imaginary
bicyclic biquadratic number fields consisting of
fields , where and are different primes. For each of the three quadratic extensions
inside the absolute genus field of , we compute the capitulation
kernel of . Then we deduce that each strongly ambiguous class of
capitulates already in , which is smaller than the relative genus
field
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