# A basis of ℤₘ, II

Colloquium Mathematicae (2007)

- Volume: 108, Issue: 1, page 141-145
- ISSN: 0010-1354

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topMin Tang, and Yong-Gao Chen. "A basis of ℤₘ, II." Colloquium Mathematicae 108.1 (2007): 141-145. <http://eudml.org/doc/283413>.

@article{MinTang2007,

abstract = {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.},

author = {Min Tang, Yong-Gao Chen},

journal = {Colloquium Mathematicae},

keywords = {Erdős–Turán conjecture; additive bases; representation function},

language = {eng},

number = {1},

pages = {141-145},

title = {A basis of ℤₘ, II},

url = {http://eudml.org/doc/283413},

volume = {108},

year = {2007},

}

TY - JOUR

AU - Min Tang

AU - Yong-Gao Chen

TI - A basis of ℤₘ, II

JO - Colloquium Mathematicae

PY - 2007

VL - 108

IS - 1

SP - 141

EP - 145

AB - 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.

LA - eng

KW - Erdős–Turán conjecture; additive bases; representation function

UR - http://eudml.org/doc/283413

ER -

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