Geodesic
Lower bounds for a conjecture of Erdős and Turán
Ioannis Konstantoulas1
1 Department of Mathematics University of Illinois 1409 W. Green St. Urbana, IL 61801, U.S.A.
Acta Arithmetica, Tome 159 (2013) no. 4, pp. 301-313

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study representation functions of asymptotic additive bases and more general subsets of $\mathbb N$ (sets with few nonrepresentable numbers). We prove that if $\mathbb N\setminus (A+A)$ 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.
DOI : 10.4064/aa159-4-1
Keywords: study representation functions asymptotic additive bases general subsets mathbb sets few nonrepresentable numbers prove mathbb setminus has sufficiently small upper density asymptotic bases there infinitely many numbers five representations counting order

Ioannis Konstantoulas 1

1 Department of Mathematics University of Illinois 1409 W. Green St. Urbana, IL 61801, U.S.A. 
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Ioannis Konstantoulas. Lower bounds for a conjecture of Erdős and Turán. Acta Arithmetica, Tome 159 (2013) no. 4, pp. 301-313. doi: 10.4064/aa159-4-1

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