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Lower bounds for a conjecture of Erdős and Turán

Volume 159 / 2013

Ioannis Konstantoulas Acta Arithmetica 159 (2013), 301-313 MSC: Primary 11B13, 11B34. DOI: 10.4064/aa159-4-1

Abstract

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.

Authors

  • Ioannis KonstantoulasDepartment of Mathematics
    University of Illinois
    1409 W. Green St.
    Urbana, IL 61801, U.S.A.
    e-mail

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