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Rosen M. gave a determinant formula for relative class numbers for the P-thcyclotomic function fields in the case of the monic irreducible polynomial P,which is regarded as an analogue of the classical Maillet determinant. In thispaper, we will give a determinant formula for the relative congruence zetafunctions for cyclotomic function fields. Our formula is regarded as ageneralization of the determinant formula for the relative class number.

A determinant formula for relative congruence zeta functions for cyclotomic function fields