A QUANTITATIVE ASPECT OF NON-UNIQUE FACTORIZATIONS: THE NARKIEWICZ CONSTANTS
Weidong Gao, Alfred Geroldinger, Qinghong Wang · International Journal of Number Theory · 2011
Let K be an algebraic number field with non-trivial class group G and let [Formula: see text] be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let Fk (x) denote the number of non-zero principal ideals [Formula: see text] with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that Fk (x) behaves, for x → ∞, asymptotically like x( log x)-1+1/|G|( log log x) N k(G). We study N k (G) with new methods from Combinatorial Number Theory.