A basis of ℤₘ, II

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

Abstrakty

EN

Given a set A ⊂ ℕ let $σ_A(n)$ denote the number of ordered pairs (a,a') ∈ A × A such that a + a' = n. Erdős and Turán conjectured that for any asymptotic basis A of ℕ, $σ_A(n)$ is unbounded. We show that the analogue of the Erdős-Turán conjecture does not hold in the abelian group (ℤₘ,+), namely, for any natural number m, there exists a set A ⊆ ℤₘ such that A + A = ℤₘ and $σ_A(n̅) ≤ 5120$ 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: 2007
• Tom: 108
• Numer: 1
• Strony: 141-145

Daty

wydano

2007

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/cm108-1-12