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Class number formulae in the form of a product of determinants in function fields

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  09 April 2009

Jaehyun Ahn ,
Soyoung Choi  and
Hwanyup Jung
Jaehyun Ahn
Affiliation:
Department of MathematicsKAIST Daejon 305-701Korea e-mail: jaehyun@math.kaist.ac.kryoung@math.kaist.ac.kr
Soyoung Choi
Affiliation:
Department of MathematicsKAIST Daejon 305-701Korea e-mail: jaehyun@math.kaist.ac.kryoung@math.kaist.ac.kr
Hwanyup Jung
Affiliation:
Department of Mathematics EducationChungbuk National UniversityCheongju Chungbuk 361-763Korea e-mail: hyjung@chungbuk.ac.kr
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Abstract

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In this paper, we generalize the Kučera's group-determinant formulae to obtain the real and relative class number formulae of any subfield of cyclotomic function fields with arbitrary conductor in the form of a product of determinants. From these formulae, we generalize the relative class number formula of Rosen and Bae-Kang and obtain analogous results of Tsumura and Hirabayashi for an intermediate field in the tower of cyclotomic function fields with prime power conductor.

Keywords

cyclotomic function fieldsclass number

MSC classification

Secondary: 11R60: Cyclotomic function fields (class groups, Bernoulli objects, etc.) 11R58: Arithmetic theory of algebraic function fields
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 2 , April 2005 , pp. 227 - 238
Copyright
Copyright © Australian Mathematical Society 2005

References

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