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Class numbers of some abelian extensions of rational function fields

Authors:	Sunghan Bae Hwanyup Jung Jaehyun Ahn

Institution:	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 $h(K_{P^n}^+)$ of Bae and Kang and the formula for $h^{-}(K_{P^n})$ of Jung and Ahn to any subfields of the cyclotomic function field $K_{P^n}.$ By using these formulas, we calculate the class numbers $h^{-}(K), h(K^+)$ of all subfields of when and $\deg(P)$ are small.

Keywords:	Class number function field

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