A note on the relative class number in function fields
Michael Rosen · Proceedings of the American Mathematical Society · 1997
Let F F be a finite field, A = F [ T ] A=F[T] , and k = F ( T ) k=F(T) . Let K m = k ( Λ m ) K_{m}=k(\Lambda _{m}) be the field extension of k k obtained by adjoining the m m -torsion on the Carlitz module. The class number h m h_{m} of K m K_{m} can be written as a product h m = h m + h m − h_{m}=h_{m}^{+}h_{m}^{-} . The number h m − h_{m}^{-} is called the relative class number. In this paper a formula for h m −