Cyclotomic units and divisibility of the class number of function fields

Jaehyun Ahn; Hwanyup Jung

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J. Korean Math. Soc. 2002; 39(5): 765-773

Printed September 1, 2002

Cyclotomic units and divisibility of the class number of function fields

Jaehyun Ahn and Hwanyup Jung

KAIST

Abstract

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Abstract

Let $k = \mathbb F_q(T)$ be a rational function field. Let $\ell$ be a prime number with $(\ell, q-1)=1.$ Let $K/k$ be an elementary abelian $\ell$-extension which is contained in some cyclotomic function field. In this paper, we study the $\ell$-divisibility of ideal class number $h_K$ of $K$ by using cyclotomic units.

Keywords: function field, class number, cyclotomic unit

MSC numbers: 11R58, 11R60