Abstract
Let M ⩾ 5 . For any odd prime power q and any prime ℓ ∤ q , we show that there are at least ( ln M ) / ( ln 5 ) + 1 pairwise coprime D ∈ F q [ T ] which are square-free and of odd degree ⩽ M, such that ℓ does not divide the class number of the complex quadratic functions fields F q ( T ) ( D ) / F q ( T ) .
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