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

Abstract

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.