A quantitative aspect of non-unique factorizations: the Narkiewicz constants II
Weidong Gao, Yuanlin Li, Jiangtao Peng (2011)
Colloquium Mathematicae
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Let K be an algebraic number field with non-trivial class group G and be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let denote the number of non-zero principal ideals with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that behaves, for x → ∞, asymptotically like . In this article, it is proved that for every prime p, , and it is also proved that if and m is large enough. In particular, it is shown...