An Elemental Erdős–kac Theorem for Algebraic Number Fields
نویسنده
چکیده
Abstract. Fix a number field K. For each nonzero α ∈ ZK , let ν(α) denote the number of distinct, nonassociate irreducible divisors of α. We show that ν(α) is normally distributed with mean proportional to (log log |N(α)|)D and standard deviation proportional to (log log |N(α)|)D−1/2. Here D, as well as the constants of proportionality, depend only on the class group of K. For example, for each fixed real λ, the proportion of α ∈ Z[ √ −5] with ν(α) ≤ 1 8 (log logN(α)) + λ
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