Targets 2007 / 2008

Our targets for 2007 / 2008

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Here we further pursue our well-known intricate targets:
  • To determine the capitulation type of the 2020 complex quadratic fields K
    with discriminant -106 < d < 0 and 3-class group of type (3,3).
    These objects were first listed in Supercomputing Centre 2006.
  • To determine the capitulation type of the 149 real quadratic fields K
    with discriminant 0 < d < 106 and 3-class group of type (3,3).
    These objects were first listed in Supercomputing Centre 2006.
Together with the 3-class numbers of the associated quadruplets (L1,…,L4) of cubic fields,
the capitulation type gives the isomorphism class of the 2-stage metabelian 3-group
G=Gal(K2|K) in CBF(m,n) of automorphisms of the 2nd Hilbert 3-class field K2 over K,
with the aid of our most recent sophisticated theorems in algebraic number theory [1].


Remarks added in 2010:



Contents and Navigation
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References:

[1] Daniel C. Mayer,
Two-Stage Towers of 3-Class Fields over Quadratic Fields,
(Latest Update)
Univ. Graz, 2008.

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contact@algebra.at
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