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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Class numbers of some abelian extensions of rational function fields


Authors: Sunghan Bae, Hwanyup Jung and Jaehyun Ahn
Journal: Math. Comp. 73 (2004), 377-386
MSC (2000): Primary 11R60, 11R29
Published electronically: April 28, 2003
MathSciNet review: 2034128
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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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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

DOI: http://dx.doi.org/10.1090/S0025-5718-03-01528-X
PII: S 0025-5718(03)01528-X
Keywords: Class number, function field
Received by editor(s): March 27, 2002
Received by editor(s) in revised form: May 20, 2002
Published electronically: April 28, 2003
Article copyright: © Copyright 2003 American Mathematical Society