Class number formulae in the form of a product of determinants in function fields
Jaehyun Ahn, Soyoung Choi, Hwanyup Jung
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Source: Crossref
Published: Apr 1, 2005
DOI: 10.1017/s1446788700008053
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Abstract 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.
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