A congruence modulo p of zeta polynomial for cyclotomic function fields

摘要

A cyclotomic function field is defined as adding torsion points of Carlitz module to the rational function field of characteristic p. Properties of these fields are remarkably similar to those of cyclotomic number fields. In 1999, L. Guo and L. Shu gave congruence relations for class numbers of cyclotomic function fields. In this paper, we will generalize these results from the view point of congruence zeta function.