2008 Year of Mathematics

Navigation Center 2008

0. Summary of recent research results 2008.
1. The impact of number theoretic data on the structure of the group Gal(K2|K),
the group of automorphisms of the 2nd Hilbert 3-class field K2 over a quadratic field K.
1.1. Theorems concerning the impact of 3-class numbers.
1.2. Theorems concerning the impact of 3-capitulation.
1.3. All known examples for principalization types.
2. p-ring spaces not only for counting dihedral fields of degree 2p.
2.1. Half-units in real quadratic fields.
2.2. Cubic extensions with conductor 3 or 9.
3. Current research concerning cyclic cubic fields.
3.1. Norms of primitive ambiguous principal ideals
in cyclic cubic fields with conductor divisible by two primes.

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