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

• Autorzy: Weidong Gao , Jiangtao Peng , Qinghai Zhong
• Języki publikacji: EN

Abstrakty

EN

Let K be an algebraic number field with non-trivial class group G and $𝓞_K$ 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 $a𝓞_K$ 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 $x(log x)^{1-1/|G|} (log log x)^{𝖭_k (G)}$. We prove, among other results, that $𝖭₁(C_{n₁} ⊕ C_{n₂}) = n₁ + n₂$ for all integers n₁,n₂ with 1 < n₁|n₂.

Kategorie tematyczne

• 11P70: Inverse problems of additive number theory, including sumsets
• 11B30: Arithmetic combinatorics; higher degree uniformity
• 11R27: Units and factorization
• 20K01: Finite abelian groups [For sumsets, see and ]

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 158
• Numer: 3
• Strony: 271-285

Daty

wydano

2013

Twórcy

autor

Weidong Gao

• Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China

autor

Jiangtao Peng

• College of Science, Civil Aviation University of China, Tianjin 300300, P.R. China

autor

Qinghai Zhong

• Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China

Identyfikatory

DOI

10.4064/aa158-3-6