We study representation functions of asymptotic additive bases and more general subsets of ℕ (sets with few nonrepresentable numbers). We prove that if ℕ∖(A+A) has sufficiently small upper density (as in the case of asymptotic bases) then there are infinitely many numbers with more than five representations in A+A, counting order.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-4-1,
author = {Ioannis Konstantoulas},
title = {Lower bounds for a conjecture of Erd\H os and Tur\'an},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {301-313},
zbl = {1298.11011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-4-1}
}
Ioannis Konstantoulas. Lower bounds for a conjecture of Erdős and Turán. Acta Arithmetica, Tome 161 (2013) pp. 301-313. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-4-1/