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Cyclotomic units and divisibility of the class number of function fields

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Abstract

Let k = mb F_q(T) be a rational function field. Let ell be aprime number with (ell, q-1)=1. Let K/k be an elementaryabelian ell-extension which is contained in some cyclotomicfunction field. In this paper, we study the ell-divisibility ofideal class number h_K of K by using cyclotomic units.

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