[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2007.44.3.499

GROUP DETERMINANT FORMULAS AND CLASS NUMBERS OF CYCLOTOMIC FIELDS

Jung, Hwan-Yup (DEPARTMENT OF MATHEMATICS EDUCATION CHUNGBUK NATIONAL UNIVERSITY)
Ahn, Jae-Hyun (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY)

Publication Information

Journal of the Korean Mathematical Society / v.44, no.3, 2007 , pp. 499-509 More about this Journal

Abstract

Let m, n be positive integers or monic polynomials in $\mathbb{F}_q[T]$ with n|m. Let $K_m\;and\;K^+_m$ be the m-th cyclotomic field and its maximal real subfield, respectively. In this paper we define two matrices $D^+_{m,n}\;and\;D^-_{m,n}$ whose determinants give us the ratios $\frac{h(\mathcal{O}_{K^+_m})}{h(\mathcal{O}_{K^+_n})}$ and $\frac{h-(\mathcal{O}_K_m)}{h-(\mathcal{O}_K_n)}$ with some factors, respectively.

Keywords

cyclotomic unit; cyclotomic function field;

Citations & Related Records

Times Cited By Web Of Science : 1 (Related Records In Web of Science)
Times Cited By SCOPUS : 0

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