On sums and products of integers

Nathanson, Melvyn

doi:10.1090/S0002-9939-97-03510-7

On sums and products of integers
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by Melvyn B. Nathanson PDF

Proc. Amer. Math. Soc. 125 (1997), 9-16 Request permission

Abstract:

Erdős and Szemerédi conjectured that if $A$ is a set of $k$ positive integers, then there must be at least $k^{2-\varepsilon }$ integers that can be written as the sum or product of two elements of $A$. Erdős and Szemerédi proved that this number must be at least $c k^{1 + \delta }$ for some $\delta > 0$ and $k \geq k_0$. In this paper it is proved that the result holds for $\delta = 1/31$.

References

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