Class Number Formulas Over Global Function Fields Original Research Article

In the classical theory of numbers, one has the famous theorem of Kummer giving the index of the cyclotomic units in the total unit group. Let A = imageq[T]. Then Rosen and Galovich showed an important analog of Kummer′s result for those abelian extensions of imageq(T) given by adjoining division values of the Carlitz module. In this paper we extend this theory to the case where A is the affine ring of a curve over imageq[ minus a rational point ∞. The analogs of the Carlitz module are the "sign-normalized" rank one Drinfeld modules of David Hayes.