Imaginary quadratic fields k with Cl_2(k) = (2,2^m) and Rank Cl_2(k^1) = 2

Details Imaginary quadratic fields k with Cl_2(k) = (2,2^m) and Rank Cl_2(k^1) = 2 Imaginary quadratic fields k with Cl_2(k) = (2,2^m) and Rank Cl_2(k^1) = 2

2000-03-27

arxiv.org/abs/math/0003244v1

Mathematics

Number Theory

Scientific paper

We classify all complex quadratic number fields with 2-class group of type
(2,2^m) whose Hilbert 2-class fields have class groups of 2-rank equal to 2.
These fields all have 2-class field tower of length 2. We still don't know
examples of fields with 2-class field tower of length 3, but the smallest
candidate is the field with discriminant -1015.

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