HILBERT 2-CLASS FIELD TOWERS OF IMAGINARY QUADRATIC FUNCTION FIELDS

Abstract

In this paper, we prove that the Hilbert 2-class field D) is infinite tower of an imaginary quadratic function field F = k( if r2(C(F )) = 4 and exactly one monic irreducible divisor of D is of odd degree, except for one type of R´edei matrix of F . We also compute the density of such imaginary quadratic function fields F .

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