  Rosen M. gave a determinant formula for relative class numbers for the P-th
cyclotomic function fields in the case of the monic irreducible polynomial P,
which is regarded as an analogue of the classical Maillet determinant. In this
paper, we will give a determinant formula for the relative congruence zeta
functions for cyclotomic function fields. Our formula is regarded as a
generalization of the determinant formula for the relative class number.
