Class numbers of some abelian extensions of rational function fields

Bae, Sunghan; Jung, Hwanyup; Ahn, Jaehyun

doi:10.1090/S0025-5718-03-01528-X

Class numbers of some abelian extensions of rational function fields
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by Sunghan Bae, Hwanyup Jung and Jaehyun Ahn PDF

Math. Comp. 73 (2004), 377-386 Request permission

Abstract:

Let $P$ 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 $K$ of the cyclotomic function field $K_{P^n}.$ By using these formulas, we calculate the class numbers $h^{-}(K), h(K^+)$ of all subfields $K$ of $K_P$ when $q$ and $\deg (P)$ are small.

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