Abstract
The notion of a ray class field, which is fundamental in Takagi’s class field theory, has no immediate analogon in the function field case. The reason for this lies in the lacking of a distinguished maximal order. In this paper I overcome this difficulty by a relative version of the notion of ray class fields to be defined for every holomorphy ring of the field. The prototype for this new notion is M. Rosen’s definition of a Hilbert class field for function fields [6].
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