Asymptotics of class number and genus for abelian extensions of an algebraic function field

Among abelian extensions of a congruence function field, an asymptotic relation of class number and genus is established: namely, for such extensions with class number h, genus g, and field of constants F, that . The proof is completely classical, employing well known results from congruence function field theory. This gives an answer to a question of E. Inaba.