A quantitative aspect of non-unique factorizations: the Narkiewicz constants III

Weidong Gao, Jiangtao Peng, and Qinghai Zhong. "A quantitative aspect of non-unique factorizations: the Narkiewicz constants III." Acta Arithmetica 158.3 (2013): 271-285. <http://eudml.org/doc/279710>.

@article{WeidongGao2013,
abstract = {Let K be an algebraic number field with non-trivial class group G and $_K$ be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let $F_k(x)$ denote the number of non-zero principal ideals $a_K$ with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that $F_k(x)$ behaves for x → ∞ asymptotically like $x(log x)^\{1-1/|G|\} (log log x)^\{_k (G)\}$. We prove, among other results, that $₁(C_\{n₁\} ⊕ C_\{n₂\}) = n₁ + n₂$ for all integers n₁,n₂ with 1 < n₁|n₂.},
author = {Weidong Gao, Jiangtao Peng, Qinghai Zhong},
journal = {Acta Arithmetica},
keywords = {non-unique factorization; zero-sum sequence; combinatorial constant},
language = {eng},
number = {3},
pages = {271-285},
title = {A quantitative aspect of non-unique factorizations: the Narkiewicz constants III},
url = {http://eudml.org/doc/279710},
volume = {158},
year = {2013},
}

TY - JOUR
AU - Weidong Gao
AU - Jiangtao Peng
AU - Qinghai Zhong
TI - A quantitative aspect of non-unique factorizations: the Narkiewicz constants III
JO - Acta Arithmetica
PY - 2013
VL - 158
IS - 3
SP - 271
EP - 285
AB - Let K be an algebraic number field with non-trivial class group G and $_K$ be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let $F_k(x)$ denote the number of non-zero principal ideals $a_K$ with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that $F_k(x)$ behaves for x → ∞ asymptotically like $x(log x)^{1-1/|G|} (log log x)^{_k (G)}$. We prove, among other results, that $₁(C_{n₁} ⊕ C_{n₂}) = n₁ + n₂$ for all integers n₁,n₂ with 1 < n₁|n₂.
LA - eng
KW - non-unique factorization; zero-sum sequence; combinatorial constant
UR - http://eudml.org/doc/279710
ER -