GROUP DETERMINANT FORMULAS AND CLASS NUMBERS OF CYCLOTOMIC FIELDS

Title & Authors
GROUP DETERMINANT FORMULAS AND CLASS NUMBERS OF CYCLOTOMIC FIELDS
Jung, Hwan-Yup; Ahn, Jae-Hyun;

Abstract
Let m, n be positive integers or monic polynomials in $\small{\mathbb{F}_q[T]}$ with n|m. Let $\small{K_m\;and\;K^+_m}$ be the m-th cyclotomic field and its maximal real subfield, respectively. In this paper we define two matrices $\small{D^+_{m,n}\;and\;D^-_{m,n}}$ whose determinants give us the ratios $\small{\frac{h(\mathcal{O}_{K^+_m})}{h(\mathcal{O}_{K^+_n})}}$ and $\small{\frac{h-(\mathcal{O}_K_m)}{h-(\mathcal{O}_K_n)}}$ with some factors, respectively.
Keywords
cyclotomic unit;cyclotomic function field;
Language
English
Cited by
1.
ON THE RATIO OF RELATIVE CONGRUENCE ZETA FUNCTIONS OF CYCLOTOMIC FUNCTION FIELDS, Journal of the Chungcheong Mathematical Society, 2016, 29, 1, 117
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