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

Published online by Cambridge University Press:  09 April 2009

Jaehyun Ahn
Affiliation:
Department of MathematicsKAIST Daejon 305-701Korea e-mail: [email protected]@math.kaist.ac.kr
Soyoung Choi
Affiliation:
Department of MathematicsKAIST Daejon 305-701Korea e-mail: [email protected]@math.kaist.ac.kr
Hwanyup Jung
Affiliation:
Department of Mathematics EducationChungbuk National UniversityCheongju Chungbuk 361-763Korea e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

References

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