A basis of Zₘ

• Autorzy: Min Tang , Yong-Gao Chen
• Języki publikacji: EN

Abstrakty

EN

Let $σ_{A}(n) = |{(a,a') ∈ A²: a + a' = n}|$, where n ∈ N and A is a subset of N. Erdős and Turán conjectured that for any basis A of order 2 of N, $σ_{A}(n)$ is unbounded. In 1990, Imre Z. Ruzsa constructed a basis A of order 2 of N for which $σ_{A}(n)$ is bounded in the square mean. In this paper, we show that there exists a positive integer m₀ such that, for any integer m ≥ m₀, we have a set A ⊂ Zₘ such that A + A = Zₘ and $σ_{A}(n̅) ≤ 768$ for all n̅ ∈ Zₘ.

Kategorie tematyczne

• 11B34: Representation functions
• 11B13: Additive bases, including sumsets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 104
• Numer: 1
• Strony: 99-103

Daty

wydano

2006

Twórcy

autor

Min Tang

• Department of Mathematics, Anhui Normal University, Wuhu 241000, China

autor

Yong-Gao Chen

• Department of Mathematics, Nanjing Normal University, Nanjing 210097, China

Identyfikatory

DOI

10.4064/cm104-1-6