A NOTE ON CYCLOTOMIC UNITS IN FUNCTION FIELDS

Abstract

Let A = Fq[T ] and k = Fq(T ). Assume q is odd, and fix a prime divisor (cid:96) of q − 1. Let P be a monic irreducible polynomial In this paper we define a in A whose degree d is divisible by (cid:96). q and {ητ i subgroup (cid:101)CF of O∗ F which is generated by F∗ : 0 ≤ i ≤ (cid:96) − 1} in F = k( (cid:96)√ F : (cid:101)CF ] = P ) and calculate the unit-index [O∗ (cid:96)(cid:96)−2h(OF ). This is a generalization of [3, Theorem 16.15].

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