J. Aust. Math. Soc.  78 (2005), 227-238

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

Jaehyun Ahn   Department of Mathematics   KAIST   Daejon 305-701   Korea   jaehyun@math.kaist.ac.kr Soyoung Choi   Department of Mathematics   KAIST   Daejon 305-701   Korea   young@math.kaist.ac.kr and Hwanyup Jung   Department of Mathematics Education   Chungbuk National University   Cheongju   Chungbuk 361-763   Korea   hyjung@chungbuk.ac.kr

Abstract

In this paper, we generalize the Kucera'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.

Download the article in PDF format (size 116 Kb)

Australian Mathematical Publishing Association Inc. ©  Australian MS