A DETERMINANT FORMULA FOR RELATIVE CONGRUENCE ZETA FUNCTIONS FOR CYCLOTOMIC FUNCTION FIELDS

Abstract

AbstractRosen gave a determinant formula for relative class numbers for cyclotomic function fields, which may be regarded as an analogue of the classical Maillet determinant. In this paper, we give a determinant formula for relative congruence zeta functions for cyclotomic function fields. Our formula may be regarded as a generalization of the determinant formula for the relative class number.