Department of Mathematics, KAIST, Daejon, 305-701 Korea ; Department of Mathematics, KAIST, Daejon, 305-701 Korea ; Department of Mathematics, KAIST, Daejon, 305-701 Korea
Abstract:
Let be a monic irreducible polynomial. In this paper we generalize the determinant formula for of Bae and Kang and the formula for of Jung and Ahn to any subfields of the cyclotomic function field By using these formulas, we calculate the class numbers of all subfields of when and are small.