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.References
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Additional Information
- Sunghan Bae
- Affiliation: Department of Mathematics, KAIST, Daejon, 305-701 Korea
- Email: shbae@math.kaist.ac.kr
- Hwanyup Jung
- Affiliation: Department of Mathematics, KAIST, Daejon, 305-701 Korea
- Email: hyjung@mathx.kaist.ac.kr
- Jaehyun Ahn
- Affiliation: Department of Mathematics, KAIST, Daejon, 305-701 Korea
- Email: jaehyun@mathx.kaist.ac.kr
- Received by editor(s): March 27, 2002
- Received by editor(s) in revised form: May 20, 2002
- Published electronically: April 28, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 377-386
- MSC (2000): Primary 11R60, 11R29
- DOI: https://doi.org/10.1090/S0025-5718-03-01528-X
- MathSciNet review: 2034128